{"id":2011,"date":"2020-08-21T19:42:01","date_gmt":"2020-08-21T23:42:01","guid":{"rendered":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/simplify-square-roots\/"},"modified":"2025-09-15T18:26:38","modified_gmt":"2025-09-15T22:26:38","slug":"simplify-square-roots","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/simplify-square-roots\/","title":{"raw":"7.5 Simplify Square Roots","rendered":"7.5 Simplify Square Roots"},"content":{"raw":"[latexpage]\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nBy the end of this section, you will be able to:\n<ul>\n \t<li>Use the Product Property to simplify square roots<\/li>\n \t<li>Use the Quotient Property to simplify square roots<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596219453\">In the last section, we estimated the square root of a number between two consecutive whole numbers. We can say that \\(\\sqrt{50}\\) is between 7 and 8. This is fairly easy to do when the numbers are small enough that we can use in <a class=\"autogenerated-content\" href=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/688\/2019\/06\/CNX_BMath_Figure_05_07_010_img.jpg\">(Simplify and Use Square Roots)<\/a>.<\/p>\n<p id=\"fs-id1169596554591\">But what if we want to estimate \\(\\sqrt{500}\\)? If we simplify the square root first, we\u2019ll be able to estimate it easily. There are other reasons, too, to simplify square roots as you\u2019ll see later in this chapter.<\/p>\n<p id=\"fs-id1169594158513\">A square root is considered <em data-effect=\"italics\">simplified<\/em> if its radicand contains no perfect square factors.<\/p>\n\n<div id=\"fs-id1169596372918\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Simplified Square Root<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\n\\(\\sqrt{a}\\) is considered simplified if \\(a\\) has no perfect square factors.\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596590358\">So \\(\\sqrt{31}\\) is simplified. But \\(\\sqrt{32}\\) is not simplified, because 16 is a perfect square factor of 32<\/p>\n\n<h1>Use the Product Property to Simplify Square Roots<\/h1>\n<p id=\"fs-id1169596652399\">The properties we will use to simplify expressions with square roots are similar to the properties of exponents. We know that \\({\\left(ab\\right)}^{m}={a}^{m}{b}^{m}\\). The corresponding property of square roots says that \\(\\sqrt{ab}=\\sqrt{a}\\cdot\\sqrt{b}\\).<\/p>\n\n<div id=\"fs-id1169594103489\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Product Property of Square Roots<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nIf <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em> are non-negative real numbers, then \\(\\sqrt{ab}=\\sqrt{a}\\cdot\\sqrt{b}\\).\n\n<\/div>\n<\/div>\nWe use the Product Property of Square Roots to remove all perfect square factors from a radical. We will show how to do this in <a class=\"autogenerated-content\" href=\"#fs-id1169594160049\">(Example 1)<\/a>.\n\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"title\">How To Use the Product Property to Simplify a Square Root<\/div>\n<div id=\"fs-id1169594160049\" data-type=\"exercise\">\n<div id=\"fs-id1169596338425\" data-type=\"problem\">\n<p id=\"fs-id1169596410889\">Simplify: \\(\\sqrt{50}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596254382\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<span id=\"fs-id1169596373145\" data-type=\"media\" data-alt=\"This figure has three columns and three rows. The first row says, \u201cStep 1. Find the largest perfect square factor of the radicand. Rewrite the radicand as a product using the perfect square factor.\u201d It then says, \u201c25 is the largest perfect square factor of 50. 50 equals 25 times 2. Always write the perfect square factor first.\u201d Then it shows the square root of 50 and the square root of 25 times 2.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_09_02_001a_img_new.jpg\" alt=\"This figure has three columns and three rows. The first row says, \u201cStep 1. Find the largest perfect square factor of the radicand. Rewrite the radicand as a product using the perfect square factor.\u201d It then says, \u201c25 is the largest perfect square factor of 50. 50 equals 25 times 2. Always write the perfect square factor first.\u201d Then it shows the square root of 50 and the square root of 25 times 2.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169596288693\" data-type=\"media\" data-alt=\"The second row says, \u201cStep 2. Use the product rule to rewrite the radical as the product of two radicals.\u201d The second column is empty, but the third column shows the square root of 25 times the square root of 2.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_09_02_001b_img_new.jpg\" alt=\"The second row says, \u201cStep 2. Use the product rule to rewrite the radical as the product of two radicals.\u201d The second column is empty, but the third column shows the square root of 25 times the square root of 2.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169596459717\" data-type=\"media\" data-alt=\"The third row says, \u201cStep 3. Simplify the square root of the perfect square.\u201d The second column is empty, but the third column shows 5 times the square root of 2.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_09_02_001c_img_new.jpg\" alt=\"The third row says, \u201cStep 3. Simplify the square root of the perfect square.\u201d The second column is empty, but the third column shows 5 times the square root of 2.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596377836\" data-type=\"problem\">\n<p id=\"fs-id1169596402880\">Simplify: \\(\\sqrt{48}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596302684\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596364674\">\\(4\\sqrt{3}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596370444\" data-type=\"problem\">\n<p id=\"fs-id1169596348918\">Simplify: \\(\\sqrt{45}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594206710\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169594052437\">\\(3\\sqrt{5}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169594052585\">Notice in the previous example that the simplified form of \\(\\sqrt{50}\\) is \\(5\\sqrt{2}\\), which is the product of an integer and a square root. We always write the integer in front of the square root.<\/p>\n\n<div id=\"fs-id1169594158886\" class=\"howto\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">HOW TO: Simplify a square root using the product property.<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1169596223029\" class=\"stepwise\" type=\"1\">\n \t<li>Find the largest perfect square factor of the radicand. Rewrite the radicand as a product using the perfect-square factor.<\/li>\n \t<li>Use the product rule to rewrite the radical as the product of two radicals.<\/li>\n \t<li>Simplify the square root of the perfect square.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596319571\" data-type=\"problem\">\n<p id=\"fs-id1169596622645\">Simplify: \\(\\sqrt{500}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596407858\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\"><\/td>\n<td style=\"width: 50%; height: 30px;\">\\(\\sqrt{500}\\)<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">Rewrite the radicand as a product using the largest perfect square factor.<\/td>\n<td style=\"width: 50%; height: 30px;\">\\(\\sqrt{100\\cdot 5}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Rewrite the radical as the product of two radicals.<\/td>\n<td style=\"width: 50%; height: 14px;\">\\(\\sqrt{100}\\cdot \\sqrt{5}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Simplify.<\/td>\n<td style=\"width: 50%; height: 14px;\">\\(10\\sqrt{5}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594177476\" data-type=\"problem\">\n<p id=\"fs-id1169596292124\">Simplify: \\(\\sqrt{288}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596655673\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596765661\">\\(12\\sqrt{2}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596387302\" data-type=\"problem\">\n<p id=\"fs-id1169594159880\">Simplify: \\(\\sqrt{432}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596373127\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596238486\">\\(12\\sqrt{3}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596406648\">We could use the simplified form \\(10\\sqrt{5}\\) to estimate \\(\\sqrt{500}\\). We know 5 is between 2 and 3, and \\(\\sqrt{500}\\) is \\(10\\sqrt{5}\\). So \\(\\sqrt{500}\\) is between 20 and 30.<\/p>\n<p id=\"fs-id1169596453704\">The next example is much like the previous examples, but with variables.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596697922\" data-type=\"problem\">\n<p id=\"fs-id1169596463666\">Simplify: \\(\\sqrt{{x}^{3}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596230922\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{{x}^{3}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radicand as a product using the largest perfect square factor.<\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{{x}^{2}\\cdot x}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radical as the product of two radicals.<\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{{x}^{2}}\\cdot\\sqrt{x}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\">\\(x\\sqrt{x}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1169596310115\">Simplify: \\(\\sqrt{{b}^{5}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596768044\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596364678\">\\({b}^{2}\\sqrt{b}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596392471\" data-type=\"problem\">\n<p id=\"fs-id1169596404923\">Simplify: \\(\\sqrt{{p}^{9}}\\).<\/p>\n\n<\/div>\n<div data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169594121898\">\\({p}^{4}\\sqrt{p}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596567681\">We follow the same procedure when there is a coefficient in the radical, too.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594189919\" data-type=\"problem\">\n<p id=\"fs-id1169596463373\">Simplify: \\(\\sqrt{25{y}^{5}.}\\)<\/p>\n\n<\/div>\n<div id=\"fs-id1169596386215\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{25{y}^{5}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radicand as a product using the largest perfect square factor.<\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{25{y}^{4}\\cdot y}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radical as the product of two radicals.<\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{25{y}^{4}}\\cdot\\sqrt{y}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\">\\(5{y}^{2}\\sqrt{y}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596299615\" data-type=\"problem\">\n<p id=\"fs-id1169594084070\">Simplify: \\(\\sqrt{16{x}^{7}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596686630\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169594050724\">\\(4{x}^{3}\\sqrt{x}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596533824\" data-type=\"problem\">\n<p id=\"fs-id1169596620153\">Simplify: \\(\\sqrt{49{v}^{9}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594095365\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596308748\">\\(7{v}^{4}\\sqrt{v}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596764345\">In the next example both the constant and the variable have perfect square factors.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596398045\" data-type=\"problem\">\n<p id=\"fs-id1169596453520\">Simplify: \\(\\sqrt{72{n}^{7}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596500662\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{72{n}^{7}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radicand as a product using the largest perfect square factor.<\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{36{n}^{6}\\cdot 2n}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radical as the product of two radicals.<\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{36{n}^{6}}\\cdot \\sqrt{2n}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\">\\(6{n}^{3}\\sqrt{2n}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596386252\" data-type=\"problem\">\n<p id=\"fs-id1169596516908\">Simplify: \\(\\sqrt{32{y}^{5}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594156731\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596386368\">\\(4{y}^{2}\\sqrt{2y}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596365414\" data-type=\"problem\">\n<p id=\"fs-id1169596390228\">Simplify: \\(\\sqrt{75{a}^{9}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596591079\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596371716\">\\(5{a}^{4}\\sqrt{3a}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596302244\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594011599\" data-type=\"exercise\">\n<div id=\"fs-id1169596591079\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594041083\" data-type=\"problem\">\n<p id=\"fs-id1169596282475\">Simplify: \\(\\sqrt{63{u}^{3}{v}^{5}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594136417\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{63{u}^{3}{v}^{5}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radicand as a product using the largest perfect square factor.<\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{9{u}^{2}{v}^{4}\\cdot 7uv}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radical as the product of two radicals.<\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{9{u}^{2}{v}^{4}}\\cdot\\sqrt{7uv}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\">\\(3u{v}^{2}\\sqrt{7uv}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596463774\" data-type=\"problem\">\n<p id=\"fs-id1169594059352\">Simplify: \\(\\sqrt{98{a}^{7}{b}^{5}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596705013\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596705016\">\\(7{a}^{3}{b}^{2}{\\sqrt{2ab}}^{}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596656241\" data-type=\"problem\">\n<p id=\"fs-id1169596500370\">Simplify: \\(\\sqrt{180{m}^{9}{n}^{11}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596296865\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\\(6{m}^{4}{n}^{5}\\sqrt{5mn}\\)\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596497614\">We have seen how to use the Order of Operations to simplify some expressions with radicals. To simplify \\(\\sqrt{25}+\\sqrt{144}\\) we must simplify each square root separately first, then add to get the sum of 17<\/p>\n<p id=\"fs-id1169596588708\">The expression \\(\\sqrt{17}+\\sqrt{7}\\) cannot be simplified\u2014to begin we\u2019d need to simplify each square root, but neither 17 nor 7 contains a perfect square factor.<\/p>\n<p id=\"fs-id1169596702528\">In the next example, we have the sum of an integer and a square root. We simplify the square root but cannot add the resulting expression to the integer.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596255871\" data-type=\"problem\">\n<p id=\"fs-id1169596255874\">Simplify: \\(3+\\sqrt{32}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594001918\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">\\(3+\\sqrt{32}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radicand as a product using the largest perfect square factor.<\/td>\n<td style=\"width: 50%;\">\\(3+\\sqrt{16\\cdot 2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radical as the product of two radicals.<\/td>\n<td style=\"width: 50%;\">\\(3+\\sqrt{16}\\cdot\\sqrt{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\">\\(3+4\\sqrt{2}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"fs-id1169596760626\">The terms are not like and so we cannot add them. Trying to add an integer and a radical is like trying to add an integer and a variable\u2014they are not like terms!<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596496979\" data-type=\"problem\">\n<p id=\"fs-id1169596496981\">Simplify: \\(5+\\sqrt{75}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594102569\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596766546\">\\(5+5\\sqrt{3}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594085109\" data-type=\"problem\">\n<p id=\"fs-id1169594085112\">Simplify: \\(2+\\sqrt{98}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594062896\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596687162\">\\(2+7\\sqrt{2}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596389998\">The next example includes a fraction with a radical in the numerator. Remember that in order to simplify a fraction you need a common factor in the numerator and denominator.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596687670\" data-type=\"problem\">\n<p id=\"fs-id1169596687672\">Simplify: \\(\\frac{4-\\sqrt{48}}{2}\\).<\/p>\n\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">\\(\\frac{4-\\sqrt{48}}{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radicand as a product using the largest perfect square factor.<\/td>\n<td style=\"width: 50%;\">\\(\\frac{4-\\sqrt{16\\cdot 3}}{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radical as the product of two radicals.<\/td>\n<td style=\"width: 50%;\">\\(\\frac{4-\\sqrt{16}\\cdot\\sqrt{3}}{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\">\\(\\frac{4-4\\sqrt{3}}{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Factor the common factor from the numerator.<\/td>\n<td style=\"width: 50%;\">\\(\\frac{4\\left(1-\\sqrt{3}\\right)}{2}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Remove the common factor, 2, from the numerator and denominator.<\/td>\n<td style=\"width: 50%;\">\\(\\frac{\\overline{)2}\\cdot 2\\left(1-\\sqrt{3}\\right)}{\\overline{)2}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\">\\(2\\left(1-\\sqrt{3}\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594287732\" data-type=\"problem\">\n<p id=\"fs-id1169594287734\">Simplify: \\(\\frac{10-\\sqrt{75}}{5}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596373694\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596373696\">\\(2-\\sqrt{3}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596499381\" data-type=\"problem\">\n<p id=\"fs-id1169596589940\">Simplify: \\(\\frac{6-\\sqrt{45}}{3}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596655108\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169596655111\">\\(2-\\sqrt{5}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<h1>Use the Quotient Property to Simplify Square Roots<\/h1>\n<p id=\"fs-id1169596756102\">Whenever you have to simplify a square root, the first step you should take is to determine whether the radicand is a perfect square. A <em data-effect=\"italics\">perfect square fraction<\/em> is a fraction in which both the numerator and the denominator are perfect squares.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594170714\" data-type=\"problem\">\n<p id=\"fs-id1169594170716\">Simplify: \\(\\sqrt{\\frac{9}{64}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596238474\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{\\frac{9}{64}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">\\(\\text{Since}{\\left(\\frac{3}{8}\\right)}^{2}=\\frac{9}{64}\\)<\/td>\n<td style=\"width: 50%;\">\\(\\frac{3}{8}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596257077\" data-type=\"problem\">\n<p id=\"fs-id1169596257079\">Simplify: \\(\\sqrt{\\frac{25}{16}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594078139\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169594078141\">\\(\\frac{5}{4}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596362897\" data-type=\"problem\">\n<p id=\"fs-id1169596362900\">Simplify: \\(\\sqrt{\\frac{49}{81}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596443300\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596443302\">\\(\\frac{7}{9}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594236086\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594236089\" data-type=\"exercise\">\n<div id=\"fs-id1169596443300\" data-type=\"solution\">\n<p id=\"fs-id1169596443302\">If the numerator and denominator have any common factors, remove them. You may find a perfect square fraction!<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596441416\" data-type=\"problem\">\n<p id=\"fs-id1169594243096\">Simplify: \\(\\sqrt{\\frac{45}{80}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594052626\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{\\frac{45}{80}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify inside the radical first. Rewrite showing the common factors of the numerator and denominator.<\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{\\frac{5\\cdot 9}{5\\cdot 16}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify the fraction by removing common factors.<\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{\\frac{9}{16}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">\\(\\text{Simplify}{\\left(\\frac{3}{4}\\right)}^{2}=\\frac{9}{16}\\)<\/td>\n<td style=\"width: 50%;\">\\(\\frac{3}{4}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596362097\" data-type=\"problem\">\n<p id=\"fs-id1169596362099\">Simplify: \\(\\sqrt{\\frac{75}{48}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594060156\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169594060158\">\\(\\frac{5}{4}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594028882\" data-type=\"problem\">\n<p id=\"fs-id1169594028884\">Simplify: \\(\\sqrt{\\frac{98}{162}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596238924\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596238926\">\\(\\frac{7}{9}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\nIn the last example, our first step was to simplify the fraction under the radical by removing common factors. In the next example we will use the Quotient Property to simplify under the radical. We divide the like bases by subtracting their exponents, \\(\\frac{{a}^{m}}{{a}^{n}}={a}^{m-n},a\\ne 0\\).\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596700036\" data-type=\"problem\">\n<p id=\"fs-id1169596700038\">Simplify: \\(\\sqrt{\\frac{{m}^{6}}{{m}^{4}}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596767506\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<td style=\"width: 50%; height: 14px;\">\\(\\sqrt{\\frac{{m}^{6}}{{m}^{4}}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 46px;\">\n<td style=\"width: 50%; height: 46px;\">Simplify the fraction inside the radical first. Divide the like bases by subtracting the exponents.<\/td>\n<td style=\"width: 50%; height: 46px;\">\\(\\sqrt{{m}^{2}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Simplify.<\/td>\n<td style=\"width: 50%; height: 14px;\">\\(m\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594083786\" data-type=\"problem\">\n<p id=\"fs-id1169596253237\">Simplify: \\(\\sqrt{\\frac{{a}^{8}}{{a}^{6}}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596397008\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169594210772\">\\(a\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596534587\" data-type=\"problem\">\n<p id=\"fs-id1169596534589\">Simplify: \\(\\sqrt{\\frac{{x}^{14}}{{x}^{10}}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594087750\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596765047\">\\({x}^{2}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596319533\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594083784\" data-type=\"exercise\">\n<div id=\"fs-id1169594083786\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594014230\" data-type=\"problem\">\n<p id=\"fs-id1169596340910\">Simplify: \\(\\sqrt{\\frac{48{p}^{7}}{3{p}^{3}}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596497884\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{\\frac{48{p}^{7}}{3{p}^{3}}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify the fraction inside the radical first.<\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{16{p}^{4}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\">\\(4{p}^{2}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596398191\" data-type=\"problem\">\n<p id=\"fs-id1169596398193\">Simplify: \\(\\sqrt{\\frac{75{x}^{5}}{3x}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594097296\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169594097298\">\\(5{x}^{2}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596701437\" data-type=\"problem\">\n<p id=\"fs-id1169596701439\">Simplify: \\(\\sqrt{\\frac{72{z}^{12}}{2{z}^{10}}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594046460\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169594046462\">\\(6z\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596658470\">Remember the Quotient to a Power Property? It said we could raise a fraction to a power by raising the numerator and denominator to the power separately.<\/p>\n\n<div id=\"fs-id1168741953417\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\({\\left(\\frac{a}{b}\\right)}^{m}=\\frac{{a}^{m}}{{b}^{m}},b\\ne 0\\)<\/div>\n<p id=\"fs-id1169596766148\">We can use a similar property to simplify a square root of a fraction. After removing all common factors from the numerator and denominator, if the fraction is not a perfect square we simplify the numerator and denominator separately.<\/p>\n\n<div id=\"fs-id1169596766153\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Quotient Property of Square Roots<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596642328\">If <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em> are non-negative real numbers and \\(b\\ne 0\\), then<\/p>\n\n<div id=\"fs-id1169596440488\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\sqrt{\\frac{a}{b}}=\\frac{\\sqrt{a}}{\\sqrt{b}}\\)<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594176074\" data-type=\"problem\">\n<p id=\"fs-id1169594176076\">Simplify: \\(\\sqrt{\\frac{21}{64}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594150320\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{\\frac{21}{64}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">We cannot simplify the fraction inside the radical. Rewrite using the quotient property.<\/td>\n<td style=\"width: 50%;\">\\(\\frac{\\sqrt{21}}{\\sqrt{64}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify the square root of 64. The numerator cannot be simplified.<\/td>\n<td style=\"width: 50%;\">\\(\\frac{\\sqrt{21}}{8}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596440488\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594160279\" data-type=\"problem\">\n<p id=\"fs-id1169594160281\">Simplify: \\(\\sqrt{\\frac{19}{49}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596394531\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596394533\">\\(\\frac{\\sqrt{19}}{7}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596540574\" data-type=\"problem\">\n<p id=\"fs-id1169596540577\">Simplify: \\(\\sqrt{\\frac{28}{81}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596589934\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596589936\">\\(\\frac{2\\sqrt{7}}{9}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596641239\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596540572\" data-type=\"exercise\">\n<div id=\"fs-id1169596589934\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"title\">How to Use the Quotient Property to Simplify a Square Root<\/div>\n<div id=\"fs-id1169594012111\" data-type=\"exercise\">\n<div id=\"fs-id1169596648392\" data-type=\"problem\">\n<p id=\"fs-id1169596648394\">Simplify: \\(\\sqrt{\\frac{27{m}^{3}}{196}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596625666\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<span id=\"fs-id1169596557582\" data-type=\"media\" data-alt=\"This table has three columns and three rows. The first row reads, \u201cStep 1. Simplify the fraction in the radicand, if possible.\u201d Then it shows that 27 m cubed over 196 cannot be simplified. Then it shows the square root of 27 m cubed over 196.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_09_02_002a_img_new.jpg\" alt=\"This table has three columns and three rows. The first row reads, \u201cStep 1. Simplify the fraction in the radicand, if possible.\u201d Then it shows that 27 m cubed over 196 cannot be simplified. Then it shows the square root of 27 m cubed over 196.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169596764915\" data-type=\"media\" data-alt=\"The second row says, \u201cStep 2. Use the Quotient Property to rewrite the radical as the quotient of two radicals.\u201d Then it says, \u201cWe rewrite the square root of 27 m cubed over 196 as the quotient of the square root of 27 m cubed and the square root of 196.\u201d Then it shows the square root of 27 m cubed over the square root of 196.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_09_02_002b_img_new.jpg\" alt=\"The second row says, \u201cStep 2. Use the Quotient Property to rewrite the radical as the quotient of two radicals.\u201d Then it says, \u201cWe rewrite the square root of 27 m cubed over 196 as the quotient of the square root of 27 m cubed and the square root of 196.\u201d Then it shows the square root of 27 m cubed over the square root of 196.\" data-media-type=\"image\/jpeg\"><\/span><span id=\"fs-id1169596382516\" data-type=\"media\" data-alt=\"The third row says, \u201cStep 3. Simplify the radicals in the numerator and the denominator.\u201d Then it says, \u201c9 m squared and 196 are perfect squares.\u201d It then shows the square root of 9 m squared time the square root of 3 m over the square root of 196. It then shows 3 m times the square root of 3 m over 14.\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_09_02_002c_img_new.jpg\" alt=\"The third row says, \u201cStep 3. Simplify the radicals in the numerator and the denominator.\u201d Then it says, \u201c9 m squared and 196 are perfect squares.\u201d It then shows the square root of 9 m squared time the square root of 3 m over the square root of 196. It then shows 3 m times the square root of 3 m over 14.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596686530\" data-type=\"problem\">\n<p id=\"fs-id1169596686533\">Simplify: \\(\\sqrt{\\frac{24{p}^{3}}{49}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594210515\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169594210517\">\\(\\frac{2p\\sqrt{6p}}{7}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596449674\" data-type=\"problem\">\n<p id=\"fs-id1169596449676\">Simplify: \\(\\sqrt{\\frac{48{x}^{5}}{100}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596308760\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596518525\">\\(\\frac{2{x}^{2}\\sqrt{3x}}{5}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">HOW TO: Simplify a square root using the quotient property.<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1169594175504\" class=\"stepwise\" type=\"1\">\n \t<li>Simplify the fraction in the radicand, if possible.<\/li>\n \t<li>Use the Quotient Property to rewrite the radical as the quotient of two radicals.<\/li>\n \t<li>Simplify the radicals in the numerator and the denominator.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596587259\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596686528\" data-type=\"exercise\">\n<div id=\"fs-id1169596686530\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596686008\" data-type=\"problem\">\n<p id=\"fs-id1169596239293\">Simplify: \\(\\sqrt{\\frac{45{x}^{5}}{{y}^{4}}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594167750\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{\\frac{45{x}^{5}}{{y}^{4}}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">We cannot simplify the fraction in the radicand. Rewrite using the Quotient Property.<\/td>\n<td style=\"width: 50%;\">\\(\\frac{\\sqrt{45{x}^{5}}}{\\sqrt{{y}^{4}}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify the radicals in the numerator and the denominator.<\/td>\n<td style=\"width: 50%;\">\\(\\frac{\\sqrt{9{x}^{4}}\\cdot\\sqrt{5x}}{{y}^{2}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\">\\(\\frac{3{x}^{2}\\sqrt{5x}}{{y}^{2}}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594171172\" data-type=\"problem\">\n<p id=\"fs-id1169594171174\">Simplify: \\(\\sqrt{\\frac{80{m}^{3}}{{n}^{6}}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596626003\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596598359\">\\(\\frac{4m\\sqrt{5m}}{{n}^{3}}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596704774\" data-type=\"problem\">\n<p id=\"fs-id1169594159672\">Simplify: \\(\\sqrt{\\frac{54{u}^{7}}{{v}^{8}}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596522185\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596522188\">\\(\\frac{3{u}^{3}\\sqrt{6u}}{{v}^{4}}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169594014279\">Be sure to simplify the fraction in the radicand first, if possible.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594212440\" data-type=\"problem\">\n<p id=\"fs-id1169594154637\">Simplify: \\(\\sqrt{\\frac{81{d}^{9}}{25{d}^{4}}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596517992\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{\\frac{81{d}^{9}}{25{d}^{4}}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify the fraction in the radicand.<\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{\\frac{81{d}^{5}}{25}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite using the Quotient Property.<\/td>\n<td style=\"width: 50%;\">\\(\\frac{\\sqrt{81{d}^{5}}}{\\sqrt{25}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify the radicals in the numerator and the denominator.<\/td>\n<td style=\"width: 50%;\">\\(\\frac{\\sqrt{81{d}^{4}}\\cdot\\sqrt{d}}{5}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\">\\(\\frac{9{d}^{2}\\sqrt{d}}{5}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594011369\" data-type=\"problem\">\n<p id=\"fs-id1169594011371\">Simplify: \\(\\sqrt{\\frac{64{x}^{7}}{9{x}^{3}}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594123346\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169594051361\">\\(\\frac{8{x}^{2}}{3}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596446742\" data-type=\"problem\">\n<p id=\"fs-id1169596446744\">Simplify: \\(\\sqrt{\\frac{16{a}^{9}}{100{a}^{5}}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594101856\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169594101859\">\\(\\frac{2{a}^{2}}{5}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594050085\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594011367\" data-type=\"exercise\">\n<div id=\"fs-id1169594011369\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 17<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596447985\" data-type=\"problem\">\n<p id=\"fs-id1169596447987\">Simplify: \\(\\sqrt{\\frac{18{p}^{5}{q}^{7}}{32p{q}^{2}}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594063563\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{\\frac{18{p}^{5}{q}^{7}}{32p{q}^{2}}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify the fraction in the radicand, if possible.<\/td>\n<td style=\"width: 50%;\">\\(\\sqrt{\\frac{9{p}^{4}{q}^{5}}{16}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite using the Quotient Property.<\/td>\n<td style=\"width: 50%;\">\\(\\frac{\\sqrt{9{p}^{4}{q}^{5}}}{\\sqrt{16}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify the radicals in the numerator and the denominator.<\/td>\n<td style=\"width: 50%;\">\\(\\frac{\\sqrt{9{p}^{4}{q}^{4}}\\cdot\\sqrt{q}}{4}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\">\\(\\frac{3{p}^{2}{q}^{2}\\sqrt{q}}{4}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 17.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594206609\" data-type=\"problem\">\n<p id=\"fs-id1169596704334\">Simplify: \\(\\sqrt{\\frac{50{x}^{5}{y}^{3}}{72{x}^{4}y}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596765965\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169596765967\">\\(\\frac{5y\\sqrt{x}}{6}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 17.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596244116\" data-type=\"problem\">\n<p id=\"fs-id1169596244118\">Simplify: \\(\\sqrt{\\frac{48{m}^{7}{n}^{2}}{125{m}^{5}{n}^{9}}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594004728\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1169594004731\">\\(\\frac{4m\\sqrt{3}}{5{n}^{3}\\sqrt{5n}}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1169594002164\" data-bullet-style=\"bullet\">\n \t<li><strong data-effect=\"bold\">Simplified Square Root<\/strong>\\(\\sqrt{a}\\) is considered simplified if \\(a\\) has no perfect-square factors.<\/li>\n \t<li><strong data-effect=\"bold\">Product Property of Square Roots<\/strong> If <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em> are non-negative real numbers, then\n<div id=\"fs-id1169594148789\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\sqrt{ab}=\\sqrt{a}\\cdot\\sqrt{b}\\)<\/div><\/li>\n \t<li><strong data-effect=\"bold\">Simplify a Square Root Using the Product Property<\/strong> To simplify a square root using the Product Property:\n<ol id=\"fs-id1169594079028\" class=\"stepwise\" type=\"1\">\n \t<li>Find the largest perfect square factor of the radicand. Rewrite the radicand as a product using the perfect square factor.<\/li>\n \t<li>Use the product rule to rewrite the radical as the product of two radicals.<\/li>\n \t<li>Simplify the square root of the perfect square.<\/li>\n<\/ol>\n<\/li>\n \t<li><strong data-effect=\"bold\">Quotient Property of Square Roots<\/strong> If <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em> are non-negative real numbers and \\(b\\ne 0\\), then\n<div id=\"fs-id1169596380046\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\sqrt{\\frac{a}{b}}=\\frac{\\sqrt{a}}{\\sqrt{b}}\\)<\/div><\/li>\n \t<li><strong data-effect=\"bold\">Simplify a Square Root Using the Quotient Property<\/strong> To simplify a square root using the Quotient Property:\n<ol id=\"fs-id1169594102064\" class=\"stepwise\" type=\"1\">\n \t<li>Simplify the fraction in the radicand, if possible.<\/li>\n \t<li>Use the Quotient Rule to rewrite the radical as the quotient of two radicals.<\/li>\n \t<li>Simplify the radicals in the numerator and the denominator.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1>Practice Makes Perfect<\/h1>\n<h2 id=\"fs-id1169594011876\">Use the Product Property to Simplify Square Roots<\/h2>\n<p id=\"fs-id1168741952304\">In the following exercises, simplify.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 378px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">1. \\(\\sqrt{27}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">2. \\(\\sqrt{80}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">3. \\(\\sqrt{125}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">4. \\(\\sqrt{96}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">5. \\(\\sqrt{200}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">6. \\(\\sqrt{147}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">7. \\(\\sqrt{450}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">8. \\(\\sqrt{252}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">9. \\(\\sqrt{800}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">10. \\(\\sqrt{288}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">11. \\(\\sqrt{675}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">12. \\(\\sqrt{1250}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">13. \\(\\sqrt{{x}^{7}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">14. \\(\\sqrt{{y}^{11}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">15. \\(\\sqrt{{p}^{3}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">16. \\(\\sqrt{{q}^{5}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">17. \\(\\sqrt{{m}^{13}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">18. \\(\\sqrt{{n}^{21}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">19. \\(\\sqrt{{r}^{25}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">20. \\(\\sqrt{{s}^{33}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">21. \\(\\sqrt{49{n}^{17}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">22. \\(\\sqrt{25{m}^{9}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">23. \\(\\sqrt{81{r}^{15}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">24. \\(\\sqrt{100{s}^{19}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">25. \\(\\sqrt{98{m}^{5}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">26. \\(\\sqrt{32{n}^{11}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">27. \\(\\sqrt{125{r}^{13}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">28. \\(\\sqrt{80{s}^{15}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">29. \\(\\sqrt{200{p}^{13}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">30. \\(\\sqrt{128{q}^{3}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">31. \\(\\sqrt{242{m}^{23}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">32. \\(\\sqrt{175{n}^{13}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">33. \\(\\sqrt{147{m}^{7}{n}^{11}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">34. \\(\\sqrt{48{m}^{7}{n}^{5}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">35.\\(\\sqrt{75{r}^{13}{s}^{9}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">36. \\(\\sqrt{96{r}^{3}{s}^{3}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">37. \\(\\sqrt{300{p}^{9}{q}^{11}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">38. \\(\\sqrt{192{q}^{3}{r}^{7}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">39. \\(\\sqrt{242{m}^{13}{n}^{21}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">40. \\(\\sqrt{150{m}^{9}{n}^{3}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">41. \\(5+\\sqrt{12}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">42. \\(8+\\sqrt{96}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">43. \\(1+\\sqrt{45}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">44. \\(3+\\sqrt{125}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">45. \\(\\frac{10-\\sqrt{24}}{2}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">46. \\(\\frac{8-\\sqrt{80}}{4}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">47. \\(\\frac{3+\\sqrt{90}}{3}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">48. \\(\\frac{15+\\sqrt{75}}{5}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169594059546\"><strong data-effect=\"bold\">\n<\/strong>Use the Quotient Property to Simplify Square Roots<\/h2>\n<p id=\"fs-id1168745119026\">In the following exercises, simplify.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 294px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">49. \\(\\sqrt{\\frac{49}{64}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">50. \\(\\sqrt{\\frac{100}{36}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">51. \\(\\sqrt{\\frac{121}{16}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">52. \\(\\sqrt{\\frac{144}{169}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">53. \\(\\sqrt{\\frac{72}{98}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">54. \\(\\sqrt{\\frac{75}{12}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">55. \\(\\sqrt{\\frac{9}{25}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">56. \\(\\sqrt{\\frac{300}{243}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">57. \\(\\sqrt{\\frac{{x}^{10}}{{x}^{6}}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">58. \\(\\sqrt{\\frac{{p}^{20}}{{p}^{10}}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">59. \\(\\sqrt{\\frac{{y}^{4}}{{y}^{8}}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">60. \\(\\sqrt{\\frac{{q}^{8}}{{q}^{14}}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">61. \\(\\sqrt{\\frac{200{x}^{7}}{2{x}^{3}}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">62. \\(\\sqrt{\\frac{98{y}^{11}}{2{y}^{5}}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">63. \\(\\sqrt{\\frac{96{p}^{9}}{6p}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">64. \\(\\sqrt{\\frac{108{q}^{10}}{3{q}^{2}}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">65. \\(\\sqrt{\\frac{36}{35}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">66. \\(\\sqrt{\\frac{144}{65}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">67. \\(\\sqrt{\\frac{20}{81}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">68. \\(\\sqrt{\\frac{21}{196}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">69. \\(\\sqrt{\\frac{96{x}^{7}}{121}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">70. \\(\\sqrt{\\frac{108{y}^{4}}{49}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">71. \\(\\sqrt{\\frac{300{m}^{5}}{64}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">72. \\(\\sqrt{\\frac{125{n}^{7}}{169}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">73. \\(\\sqrt{\\frac{98{r}^{5}}{100}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">74. \\(\\sqrt{\\frac{180{s}^{10}}{144}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">75. \\(\\sqrt{\\frac{28{q}^{6}}{225}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">76. \\(\\sqrt{\\frac{150{r}^{3}}{256}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">77. \\(\\sqrt{\\frac{75{r}^{9}}{{s}^{8}}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">78. \\(\\sqrt{\\frac{72{x}^{5}}{{y}^{6}}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">79. \\(\\sqrt{\\frac{28{p}^{7}}{{q}^{2}}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">80. \\(\\sqrt{\\frac{45{r}^{3}}{{s}^{10}}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">81. \\(\\sqrt{\\frac{100{x}^{5}}{36{x}^{3}}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">82. \\(\\sqrt{\\frac{49{r}^{12}}{16{r}^{6}}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">83. \\(\\sqrt{\\frac{121{p}^{5}}{81{p}^{2}}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">84. \\(\\sqrt{\\frac{25{r}^{8}}{64r}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">85. \\(\\sqrt{\\frac{32{x}^{5}{y}^{3}}{18{x}^{3}y}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">86. \\(\\sqrt{\\frac{75{r}^{6}{s}^{8}}{48r{s}^{4}}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">87. \\(\\sqrt{\\frac{27{p}^{2}q}{108{p}^{5}{q}^{3}}}\\)<\/td>\n<td style=\"width: 50%; height: 14px;\">88. \\(\\sqrt{\\frac{50{r}^{5}{s}^{2}}{128{r}^{2}{s}^{5}}}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 data-type=\"title\">Everyday Math<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">89.\n\na) Elliott decides to construct a square garden that will take up 288 square feet of his yard. Simplify \\(\\sqrt{288}\\) to determine the length and the width of his garden. Round to the nearest tenth of a foot.\n\nb) Suppose Elliott decides to reduce the size of his square garden so that he can create a 5-foot-wide walking path on the north and east sides of the garden. Simplify \\(\\sqrt{288}-5\\) to determine the length and width of the new garden. Round to the nearest tenth of a foot.<\/td>\n<td style=\"width: 50%;\">90.\n\na) Melissa accidentally drops a pair of sunglasses from the top of a roller coaster, 64 feet above the ground. Simplify \\(\\sqrt{\\frac{64}{16}}\\) to determine the number of seconds it takes for the sunglasses to reach the ground.\n\nb) Suppose the sunglasses in the previous example were dropped from a height of 144 feet. Simplify \\(\\sqrt{\\frac{144}{16}}\\) to determine the number of seconds it takes for the sunglasses to reach the ground.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 data-type=\"title\">Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">91. Explain why \\(\\sqrt{{x}^{4}}={x}^{2}\\). Then explain why \\(\\sqrt{{x}^{16}}={x}^{8}\\).<\/td>\n<td style=\"width: 50%;\">92. Explain why \\(7+\\sqrt{9}\\) is not equal to \\(\\sqrt{7+9}\\).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%; height: 208px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">1. \\(3\\sqrt{3}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">3. \\(5\\sqrt{5}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">5. \\(10\\sqrt{2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">7. \\(15\\sqrt{2}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">9. \\(20\\sqrt{2}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">11. \\(15\\sqrt{3}\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">13. \\({x}^{3}\\sqrt{x}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">15. \\(p\\sqrt{p}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">17. \\({m}^{6}\\sqrt{m}\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">19. \\({r}^{12}\\sqrt{r}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">21. \\(7{n}^{8}\\sqrt{n}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">23. \\(9{r}^{7}\\sqrt{r}\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">25. \\(7{m}^{2}\\sqrt{2m}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">27. \\(5{r}^{6}\\sqrt{5r}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">29. \\(10{p}^{6}\\sqrt{2p}\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">31. \\(11{m}^{11}\\sqrt{2m}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">33. \\(7{m}^{3}{n}^{5}\\sqrt{3mn}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">35. \\(5{r}^{6}{s}^{4}\\sqrt{3rs}\\) 70)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">37. \\(10{p}^{4}{q}^{5}\\sqrt{3pq}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">39. \\(11{m}^{6}{n}^{10}\\sqrt{2mn}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">41. \\(5+2\\sqrt{3}\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">43. \\(1+3\\sqrt{5}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">45. \\(5-2\\sqrt{6}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">47. \\(1+\\sqrt{10}\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">49. \\(\\frac{7}{8}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">51. \\(\\frac{11}{4}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">53. \\(\\frac{6}{7}\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">55. \\(\\frac{3}{5}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">57. \\({x}^{2}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">59. \\(\\frac{1}{{y}^{2}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">61. \\(10{x}^{2}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">63. \\(4{p}^{4}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">65. \\(\\frac{6}{\\sqrt{35}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">67. \\(\\frac{2\\sqrt{5}}{9}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">69. \\(\\frac{4{x}^{3}\\sqrt{6x}}{11}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">71. \\(\\frac{10{m}^{2}\\sqrt{3m}}{8}\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">73. \\(\\frac{7{r}^{2}\\sqrt{2r}}{10}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">75. \\(\\frac{2{q}^{3}\\sqrt{7}}{15}\\)<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">77. \\(\\frac{5{r}^{4}\\sqrt{3r}}{{s}^{4}}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">79. \\(\\frac{4{p}^{3}\\sqrt{7p}}{q}\\)<\/td>\n<td style=\"width: 33.3333%;\">81. \\(\\frac{5x}{3}\\)<\/td>\n<td style=\"width: 33.3333%;\">83. \\(\\frac{11p\\sqrt{p}}{9}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">85. \\(\\frac{4xy}{3}\\)<\/td>\n<td style=\"width: 33.3333%;\">87. \\(\\frac{1}{2pq\\sqrt{p}}\\)<\/td>\n<td style=\"width: 33.3333%;\">89. a)\\(17.0\\phantom{\\rule{0.2em}{0ex}}\\text{feet}\\)b)\\(15.0\\phantom{\\rule{0.2em}{0ex}}\\text{feet}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">91.\u00a0Answers will vary.<\/td>\n<td style=\"width: 33.3333%;\"><\/td>\n<td style=\"width: 33.3333%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\nThis chapter has been adapted from \u201cSimplify Square Roots\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<!-- pb_fixme -->","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Use the Product Property to simplify square roots<\/li>\n<li>Use the Quotient Property to simplify square roots<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596219453\">In the last section, we estimated the square root of a number between two consecutive whole numbers. We can say that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2594c1da56bc3ebdceeb9c563cb0bd32_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"32\" style=\"vertical-align: -2px;\" \/> is between 7 and 8. This is fairly easy to do when the numbers are small enough that we can use in <a class=\"autogenerated-content\" href=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/uploads\/sites\/688\/2019\/06\/CNX_BMath_Figure_05_07_010_img.jpg\">(Simplify and Use Square Roots)<\/a>.<\/p>\n<p id=\"fs-id1169596554591\">But what if we want to estimate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-da93d061665db5b5ec3bffebbfd297b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/>? If we simplify the square root first, we\u2019ll be able to estimate it easily. There are other reasons, too, to simplify square roots as you\u2019ll see later in this chapter.<\/p>\n<p id=\"fs-id1169594158513\">A square root is considered <em data-effect=\"italics\">simplified<\/em> if its radicand contains no perfect square factors.<\/p>\n<div id=\"fs-id1169596372918\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Simplified Square Root<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fc3feabd59870f8b605474392224184c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"24\" style=\"vertical-align: -4px;\" \/> is considered simplified if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> has no perfect square factors.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596590358\">So <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38c272b59b0536667645904016af78f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"32\" style=\"vertical-align: -2px;\" \/> is simplified. But <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5dc959466224c0b86affaf4fdca50fef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"32\" style=\"vertical-align: -2px;\" \/> is not simplified, because 16 is a perfect square factor of 32<\/p>\n<h1>Use the Product Property to Simplify Square Roots<\/h1>\n<p id=\"fs-id1169596652399\">The properties we will use to simplify expressions with square roots are similar to the properties of exponents. We know that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f7ed42a6ae5889598c964652c0808f69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#109;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#123;&#98;&#125;&#94;&#123;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"109\" style=\"vertical-align: -4px;\" \/>. The corresponding property of square roots says that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6ff242883a3900afc247a1a5f1d120ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#97;&#98;&#125;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#97;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#115;&#113;&#114;&#116;&#123;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"114\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<div id=\"fs-id1169594103489\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Product Property of Square Roots<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>If <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em> are non-negative real numbers, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6ff242883a3900afc247a1a5f1d120ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#97;&#98;&#125;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#97;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#115;&#113;&#114;&#116;&#123;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"114\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<p>We use the Product Property of Square Roots to remove all perfect square factors from a radical. We will show how to do this in <a class=\"autogenerated-content\" href=\"#fs-id1169594160049\">(Example 1)<\/a>.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"title\">How To Use the Product Property to Simplify a Square Root<\/div>\n<div id=\"fs-id1169594160049\" data-type=\"exercise\">\n<div id=\"fs-id1169596338425\" data-type=\"problem\">\n<p id=\"fs-id1169596410889\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2594c1da56bc3ebdceeb9c563cb0bd32_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"32\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596254382\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p><span id=\"fs-id1169596373145\" data-type=\"media\" data-alt=\"This figure has three columns and three rows. The first row says, \u201cStep 1. Find the largest perfect square factor of the radicand. Rewrite the radicand as a product using the perfect square factor.\u201d It then says, \u201c25 is the largest perfect square factor of 50. 50 equals 25 times 2. Always write the perfect square factor first.\u201d Then it shows the square root of 50 and the square root of 25 times 2.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_ElemAlg_Figure_09_02_001a_img_new.jpg\" alt=\"This figure has three columns and three rows. The first row says, \u201cStep 1. Find the largest perfect square factor of the radicand. Rewrite the radicand as a product using the perfect square factor.\u201d It then says, \u201c25 is the largest perfect square factor of 50. 50 equals 25 times 2. Always write the perfect square factor first.\u201d Then it shows the square root of 50 and the square root of 25 times 2.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169596288693\" data-type=\"media\" data-alt=\"The second row says, \u201cStep 2. Use the product rule to rewrite the radical as the product of two radicals.\u201d The second column is empty, but the third column shows the square root of 25 times the square root of 2.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_09_02_001b_img_new.jpg\" alt=\"The second row says, \u201cStep 2. Use the product rule to rewrite the radical as the product of two radicals.\u201d The second column is empty, but the third column shows the square root of 25 times the square root of 2.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169596459717\" data-type=\"media\" data-alt=\"The third row says, \u201cStep 3. Simplify the square root of the perfect square.\u201d The second column is empty, but the third column shows 5 times the square root of 2.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_09_02_001c_img_new.jpg\" alt=\"The third row says, \u201cStep 3. Simplify the square root of the perfect square.\u201d The second column is empty, but the third column shows 5 times the square root of 2.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596377836\" data-type=\"problem\">\n<p id=\"fs-id1169596402880\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c23f3bae0f8d3f66172f5c656b7a2576_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#52;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"32\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596302684\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596364674\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-53b1a8242d11842f2d674348e7043fe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"33\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596370444\" data-type=\"problem\">\n<p id=\"fs-id1169596348918\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ab3eaa0a92db99c2b4be38b81011c356_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#52;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"32\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594206710\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169594052437\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ef46a6bc8cb8a8c094ebe79d974b6bd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"33\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169594052585\">Notice in the previous example that the simplified form of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2594c1da56bc3ebdceeb9c563cb0bd32_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"32\" style=\"vertical-align: -2px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-be94847a6619797425ef1945f533df4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"33\" style=\"vertical-align: -2px;\" \/>, which is the product of an integer and a square root. We always write the integer in front of the square root.<\/p>\n<div id=\"fs-id1169594158886\" class=\"howto\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">HOW TO: Simplify a square root using the product property.<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1169596223029\" class=\"stepwise\" type=\"1\">\n<li>Find the largest perfect square factor of the radicand. Rewrite the radicand as a product using the perfect-square factor.<\/li>\n<li>Use the product rule to rewrite the radical as the product of two radicals.<\/li>\n<li>Simplify the square root of the perfect square.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596319571\" data-type=\"problem\">\n<p id=\"fs-id1169596622645\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-da93d061665db5b5ec3bffebbfd297b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596407858\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\"><\/td>\n<td style=\"width: 50%; height: 30px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-da93d061665db5b5ec3bffebbfd297b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 50%; height: 30px;\">Rewrite the radicand as a product using the largest perfect square factor.<\/td>\n<td style=\"width: 50%; height: 30px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0550205678f980caaa3a4ee5588effe3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#48;&#48;&#92;&#99;&#100;&#111;&#116;&#32;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Rewrite the radical as the product of two radicals.<\/td>\n<td style=\"width: 50%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9b462ceddfd8535d326dbd67f53137e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#48;&#48;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"77\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Simplify.<\/td>\n<td style=\"width: 50%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4da0a70cf71e25856f6796b712f102a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594177476\" data-type=\"problem\">\n<p id=\"fs-id1169596292124\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a642ba7178048ea82da606df087636e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#56;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596655673\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596765661\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b911b54fa839bbeafdc138ea73b9890e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596387302\" data-type=\"problem\">\n<p id=\"fs-id1169594159880\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ac12b2451564459c523248e477b2fb74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#52;&#51;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596373127\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596238486\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3ef7da6abcfcc35e628bb6c12e1035b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596406648\">We could use the simplified form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4da0a70cf71e25856f6796b712f102a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/> to estimate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-da93d061665db5b5ec3bffebbfd297b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/>. We know 5 is between 2 and 3, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-da93d061665db5b5ec3bffebbfd297b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4da0a70cf71e25856f6796b712f102a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/>. So <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-da93d061665db5b5ec3bffebbfd297b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/> is between 20 and 30.<\/p>\n<p id=\"fs-id1169596453704\">The next example is much like the previous examples, but with variables.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596697922\" data-type=\"problem\">\n<p id=\"fs-id1169596463666\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-92c46a31561ee51946a45895f7a8b9cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"32\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596230922\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-92c46a31561ee51946a45895f7a8b9cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"32\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radicand as a product using the largest perfect square factor.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6700a6bf0248be8b524c760a77330c0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"55\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radical as the product of two radicals.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8b2b67d4055c5a85c2fb61797d29a102_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"70\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0690d654cd65f27ee6e754f06c1cf0f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"36\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1169596310115\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-047af998e2d17e9811f705c6357a7320_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#123;&#98;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"30\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596768044\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596364678\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6781b3bc2235a6d6ef2fc8f6425800d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596392471\" data-type=\"problem\">\n<p id=\"fs-id1169596404923\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8e6452a3994e1fbbaef632237ee32a4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#123;&#112;&#125;&#94;&#123;&#57;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"34\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169594121898\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0b7f9bcb5fe640d11945db7e37125210_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#112;&#125;&#94;&#123;&#52;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#112;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"41\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596567681\">We follow the same procedure when there is a coefficient in the radical, too.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594189919\" data-type=\"problem\">\n<p id=\"fs-id1169596463373\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d98fec9a37683dc7288c6956cf30635a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#53;&#123;&#121;&#125;&#94;&#123;&#53;&#125;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"57\" style=\"vertical-align: -5px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1169596386215\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bccddcd9ed258cb0125580519619ead5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#53;&#123;&#121;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"52\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radicand as a product using the largest perfect square factor.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-06c6ce1d170ebd3006f4a6cf159e7d57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#53;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"74\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radical as the product of two radicals.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-80b7df70fcebdf44b9a948f854d32135_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#53;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#115;&#113;&#114;&#116;&#123;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"89\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f84a37d903b25731ceef8052f5b6b767_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"51\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596299615\" data-type=\"problem\">\n<p id=\"fs-id1169594084070\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-47872a9dc366f6be32fe252e59513d58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#54;&#123;&#120;&#125;&#94;&#123;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"50\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596686630\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169594050724\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f95da5f0b67cae9fb5b46517f4e16f48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596533824\" data-type=\"problem\">\n<p id=\"fs-id1169596620153\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7e14da9c3b8d7c8a14fd1cf6a3425a6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#52;&#57;&#123;&#118;&#125;&#94;&#123;&#57;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"49\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594095365\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596308748\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-750e0c00678646ab667e95af833c268f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#123;&#118;&#125;&#94;&#123;&#52;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#118;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596764345\">In the next example both the constant and the variable have perfect square factors.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596398045\" data-type=\"problem\">\n<p id=\"fs-id1169596453520\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4f3ad32374b04567aef1925be539d05e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#55;&#50;&#123;&#110;&#125;&#94;&#123;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596500662\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4f3ad32374b04567aef1925be539d05e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#55;&#50;&#123;&#110;&#125;&#94;&#123;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radicand as a product using the largest perfect square factor.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5e12e14fc6d54d60d319ed6efc6d7a1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#54;&#123;&#110;&#125;&#94;&#123;&#54;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"83\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radical as the product of two radicals.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e5b904acf55db8edf6677f23a9647228_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#54;&#123;&#110;&#125;&#94;&#123;&#54;&#125;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-959b15b3555186d7fd6faa3fc98a8bde_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#110;&#125;&#94;&#123;&#51;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"62\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596386252\" data-type=\"problem\">\n<p id=\"fs-id1169596516908\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2ec79eb69344580622489152e6cb38d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#50;&#123;&#121;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"52\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594156731\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596386368\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-27dd5f251bfa12847320527444ee61e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596365414\" data-type=\"problem\">\n<p id=\"fs-id1169596390228\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-990483b909e3f1890e44334ba1fc5128_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#55;&#53;&#123;&#97;&#125;&#94;&#123;&#57;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"49\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596591079\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596371716\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bc3819b60138979404c4b166d3dfb37e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#97;&#125;&#94;&#123;&#52;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"60\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596302244\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594011599\" data-type=\"exercise\">\n<div id=\"fs-id1169596591079\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594041083\" data-type=\"problem\">\n<p id=\"fs-id1169596282475\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c58df30c436f194906a4cc3235779864_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#54;&#51;&#123;&#117;&#125;&#94;&#123;&#51;&#125;&#123;&#118;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"67\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594136417\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c58df30c436f194906a4cc3235779864_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#54;&#51;&#123;&#117;&#125;&#94;&#123;&#51;&#125;&#123;&#118;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"67\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radicand as a product using the largest perfect square factor.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cffc9ef651a7532097e67c7d0ec6c7cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#57;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#123;&#118;&#125;&#94;&#123;&#52;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#55;&#117;&#118;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"99\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radical as the product of two radicals.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e7bddd367b52ae1330328c2b04a1c523_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#57;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#123;&#118;&#125;&#94;&#123;&#52;&#125;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#115;&#113;&#114;&#116;&#123;&#55;&#117;&#118;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"114\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-20c308dc322cb0c96546e8f7d4279ae8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#117;&#123;&#118;&#125;&#94;&#123;&#50;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#55;&#117;&#118;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"80\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596463774\" data-type=\"problem\">\n<p id=\"fs-id1169594059352\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-818444c50fb844812a68cd37d660f35d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#57;&#56;&#123;&#97;&#125;&#94;&#123;&#55;&#125;&#123;&#98;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596705013\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596705016\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c5ceb46a6ad324d82319b940397c3af4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#123;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#97;&#98;&#125;&#125;&#94;&#123;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"82\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596656241\" data-type=\"problem\">\n<p id=\"fs-id1169596500370\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-92a27dc4d9d2f6d0c3bed18e7d173285_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#56;&#48;&#123;&#109;&#125;&#94;&#123;&#57;&#125;&#123;&#110;&#125;&#94;&#123;&#49;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"90\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596296865\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9e01352743b9a3e2b6686c8a62f88fe0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#109;&#125;&#94;&#123;&#52;&#125;&#123;&#110;&#125;&#94;&#123;&#53;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#109;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"101\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596497614\">We have seen how to use the Order of Operations to simplify some expressions with radicals. To simplify <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e880c444afedd5c7e7f54bb030b0ac26_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#53;&#125;&#43;&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#52;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"95\" style=\"vertical-align: -2px;\" \/> we must simplify each square root separately first, then add to get the sum of 17<\/p>\n<p id=\"fs-id1169596588708\">The expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ecb2eb6a979797965be6ddae551221c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#55;&#125;&#43;&#92;&#115;&#113;&#114;&#116;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"77\" style=\"vertical-align: -2px;\" \/> cannot be simplified\u2014to begin we\u2019d need to simplify each square root, but neither 17 nor 7 contains a perfect square factor.<\/p>\n<p id=\"fs-id1169596702528\">In the next example, we have the sum of an integer and a square root. We simplify the square root but cannot add the resulting expression to the integer.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596255871\" data-type=\"problem\">\n<p id=\"fs-id1169596255874\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e1a6e2028786f0d9049dc83098672816_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#43;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594001918\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e1a6e2028786f0d9049dc83098672816_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#43;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radicand as a product using the largest perfect square factor.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b3fd9e7eba4162df5e2384e1f641c62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#43;&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#54;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"85\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radical as the product of two radicals.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a22a22a02c5e6edca77f60d9bb8dd2dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#43;&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#54;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"100\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9d929d888888794b75357c70f845bffd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#43;&#52;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"fs-id1169596760626\">The terms are not like and so we cannot add them. Trying to add an integer and a radical is like trying to add an integer and a variable\u2014they are not like terms!<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596496979\" data-type=\"problem\">\n<p id=\"fs-id1169596496981\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e7fddda930888a6f92c58e6471796c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#43;&#92;&#115;&#113;&#114;&#116;&#123;&#55;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594102569\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596766546\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-97869f9dafe6c20ab732138840969279_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#43;&#53;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594085109\" data-type=\"problem\">\n<p id=\"fs-id1169594085112\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-61a698a3d98376d9296a2f7693096e5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#43;&#92;&#115;&#113;&#114;&#116;&#123;&#57;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594062896\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596687162\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8acfeb38192cb0df802b16c2cb807ef9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#43;&#55;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596389998\">The next example includes a fraction with a radical in the numerator. Remember that in order to simplify a fraction you need a common factor in the numerator and denominator.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596687670\" data-type=\"problem\">\n<p id=\"fs-id1169596687672\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-429537c1b2cd0812ecb43c28b19788a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#45;&#92;&#115;&#113;&#114;&#116;&#123;&#52;&#56;&#125;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"43\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-429537c1b2cd0812ecb43c28b19788a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#45;&#92;&#115;&#113;&#114;&#116;&#123;&#52;&#56;&#125;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"43\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radicand as a product using the largest perfect square factor.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9ace68ec9e5d8afb1d8cbadb25c65e95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#45;&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#54;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#125;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"54\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite the radical as the product of two radicals.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-98a85da8bd28d364dc6adead5aa289fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#45;&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#54;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#125;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"65\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ca43b0e9147355a00fbf472b1f26906d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#45;&#52;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#125;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"43\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Factor the common factor from the numerator.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-978b738dbd65449bc1dfe12ba7dc3100_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#45;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"57\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Remove the common factor, 2, from the numerator and denominator.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-06fc2a2a208732e3ed0b6c36f1c50bec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#45;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"73\" style=\"vertical-align: -13px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3070d566435525d8b01c2432d4888140_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#45;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"80\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594287732\" data-type=\"problem\">\n<p id=\"fs-id1169594287734\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f14aeeb2f025343bdeab3d73e39c63f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#45;&#92;&#115;&#113;&#114;&#116;&#123;&#55;&#53;&#125;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"50\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596373694\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596373696\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-094f8d137e582569f029b7c13096296e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#45;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"54\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596499381\" data-type=\"problem\">\n<p id=\"fs-id1169596589940\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2dd4af63a363c1d025a53cd960bb6abf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#45;&#92;&#115;&#113;&#114;&#116;&#123;&#52;&#53;&#125;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"43\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596655108\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596655111\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cc88e69004ec906ebfa0a1dc0f79cc91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#45;&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"54\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Use the Quotient Property to Simplify Square Roots<\/h1>\n<p id=\"fs-id1169596756102\">Whenever you have to simplify a square root, the first step you should take is to determine whether the radicand is a perfect square. A <em data-effect=\"italics\">perfect square fraction<\/em> is a fraction in which both the numerator and the denominator are perfect squares.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594170714\" data-type=\"problem\">\n<p id=\"fs-id1169594170716\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-57e18edfabd7e7a91b30614f9d90d68e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#54;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"35\" style=\"vertical-align: -11px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596238474\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-57e18edfabd7e7a91b30614f9d90d68e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#54;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"35\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-22449584ed857aedd9e117ec99b748d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#105;&#110;&#99;&#101;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#56;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#54;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"115\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a50f9f96c608e65c404d41e0ef6f8a47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596257077\" data-type=\"problem\">\n<p id=\"fs-id1169596257079\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d5cf290680fcc10052e9850679a913c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#53;&#125;&#123;&#49;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"35\" style=\"vertical-align: -11px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594078139\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169594078141\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-27f26f48f049d16d7bf76d51e1f91cef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596362897\" data-type=\"problem\">\n<p id=\"fs-id1169596362900\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b2ae3cf7cb3906483074ecec9aa842cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#57;&#125;&#123;&#56;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"35\" style=\"vertical-align: -11px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596443300\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596443302\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7e8ce2f90e409bd9f90b29b7e9dacb23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594236086\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594236089\" data-type=\"exercise\">\n<div id=\"fs-id1169596443300\" data-type=\"solution\">\n<p id=\"fs-id1169596443302\">If the numerator and denominator have any common factors, remove them. You may find a perfect square fraction!<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596441416\" data-type=\"problem\">\n<p id=\"fs-id1169594243096\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f1c2b18ff9a28a9379024593eb7535c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#53;&#125;&#123;&#56;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"35\" style=\"vertical-align: -11px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594052626\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f1c2b18ff9a28a9379024593eb7535c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#53;&#125;&#123;&#56;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"35\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify inside the radical first. Rewrite showing the common factors of the numerator and denominator.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0356cef7c4f5a4566197377d0ce21214_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#92;&#99;&#100;&#111;&#116;&#32;&#57;&#125;&#123;&#53;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"46\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify the fraction by removing common factors.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3c522f31cc43d7b035c97fbfe6a0ac00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#49;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"35\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ee4be193e7ff9c903873319391cd8834_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#105;&#109;&#112;&#108;&#105;&#102;&#121;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#49;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"138\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-469181e98c8ec4b1bce8f57ea4ba4e31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596362097\" data-type=\"problem\">\n<p id=\"fs-id1169596362099\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-040861072d2523eae86c89993e85ad33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#53;&#125;&#123;&#52;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"35\" style=\"vertical-align: -11px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594060156\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169594060158\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-27f26f48f049d16d7bf76d51e1f91cef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594028882\" data-type=\"problem\">\n<p id=\"fs-id1169594028884\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dd28af6428a74d33845c77aac4214f74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#56;&#125;&#123;&#49;&#54;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"42\" style=\"vertical-align: -11px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596238924\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596238926\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7e8ce2f90e409bd9f90b29b7e9dacb23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>In the last example, our first step was to simplify the fraction under the radical by removing common factors. In the next example we will use the Quotient Property to simplify under the radical. We divide the like bases by subtracting their exponents, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-50f406566552d675c6806b3f0574496a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#110;&#125;&#125;&#61;&#123;&#97;&#125;&#94;&#123;&#109;&#45;&#110;&#125;&#44;&#97;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"136\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596700036\" data-type=\"problem\">\n<p id=\"fs-id1169596700038\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-77fa544a5f45e418f997f466f4a531e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#109;&#125;&#94;&#123;&#54;&#125;&#125;&#123;&#123;&#109;&#125;&#94;&#123;&#52;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"40\" style=\"vertical-align: -11px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596767506\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<td style=\"width: 50%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-77fa544a5f45e418f997f466f4a531e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#109;&#125;&#94;&#123;&#54;&#125;&#125;&#123;&#123;&#109;&#125;&#94;&#123;&#52;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"40\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 46px;\">\n<td style=\"width: 50%; height: 46px;\">Simplify the fraction inside the radical first. Divide the like bases by subtracting the exponents.<\/td>\n<td style=\"width: 50%; height: 46px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-20b6796cd65d6ace6ec5de67299c8b6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Simplify.<\/td>\n<td style=\"width: 50%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594083786\" data-type=\"problem\">\n<p id=\"fs-id1169596253237\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-558773442cca39012e76f152c1f3b4fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#56;&#125;&#125;&#123;&#123;&#97;&#125;&#94;&#123;&#54;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"35\" style=\"vertical-align: -11px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596397008\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169594210772\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596534587\" data-type=\"problem\">\n<p id=\"fs-id1169596534589\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e1444b3d2a829a2d5224324cf332cf81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#49;&#52;&#125;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#49;&#48;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"42\" style=\"vertical-align: -11px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594087750\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596765047\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b40448f90dbf1bf9cce1035e2f3b1120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596319533\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594083784\" data-type=\"exercise\">\n<div id=\"fs-id1169594083786\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594014230\" data-type=\"problem\">\n<p id=\"fs-id1169596340910\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-804a2fcbcdaa3a59beff99575d85563f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#56;&#123;&#112;&#125;&#94;&#123;&#55;&#125;&#125;&#123;&#51;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"49\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596497884\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-804a2fcbcdaa3a59beff99575d85563f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#56;&#123;&#112;&#125;&#94;&#123;&#55;&#125;&#125;&#123;&#51;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"49\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify the fraction inside the radical first.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9912cd6118682692f0c7fe0d0c71504f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#54;&#123;&#112;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"52\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-79c43df4ddba6fc40f0bbd41c3456fb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#112;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"25\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596398191\" data-type=\"problem\">\n<p id=\"fs-id1169596398193\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ffd8cd1b64f2b4dd7ecd36e946335677_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#53;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#51;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"50\" style=\"vertical-align: -11px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594097296\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169594097298\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-baa0c10f3b651189378ee7bb755eaf94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596701437\" data-type=\"problem\">\n<p id=\"fs-id1169596701439\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-06d3a8d105abf212915e872196999f67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#50;&#123;&#122;&#125;&#94;&#123;&#49;&#50;&#125;&#125;&#123;&#50;&#123;&#122;&#125;&#94;&#123;&#49;&#48;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"55\" style=\"vertical-align: -11px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594046460\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169594046462\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-54e651f7636891b3f5a562ae5e3f2d25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#122;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596658470\">Remember the Quotient to a Power Property? It said we could raise a fraction to a power by raising the numerator and denominator to the power separately.<\/p>\n<div id=\"fs-id1168741953417\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cb4d741eab395fb1060fe7db2c499cc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#109;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#97;&#125;&#94;&#123;&#109;&#125;&#125;&#123;&#123;&#98;&#125;&#94;&#123;&#109;&#125;&#125;&#44;&#98;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"133\" style=\"vertical-align: -7px;\" \/><\/div>\n<p id=\"fs-id1169596766148\">We can use a similar property to simplify a square root of a fraction. After removing all common factors from the numerator and denominator, if the fraction is not a perfect square we simplify the numerator and denominator separately.<\/p>\n<div id=\"fs-id1169596766153\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Quotient Property of Square Roots<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596642328\">If <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em> are non-negative real numbers and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1edd53778d94abb1dc1e19acff79e9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"40\" style=\"vertical-align: -4px;\" \/>, then<\/p>\n<div id=\"fs-id1169596440488\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eb22982ecd74816acc96edd972c29616_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#115;&#113;&#114;&#116;&#123;&#97;&#125;&#125;&#123;&#92;&#115;&#113;&#114;&#116;&#123;&#98;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"73\" style=\"vertical-align: -11px;\" \/><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594176074\" data-type=\"problem\">\n<p id=\"fs-id1169594176076\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9e3b6598d742b336a4d9a189a103b433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#49;&#125;&#123;&#54;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"35\" style=\"vertical-align: -11px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594150320\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9e3b6598d742b336a4d9a189a103b433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#49;&#125;&#123;&#54;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"35\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">We cannot simplify the fraction inside the radical. Rewrite using the quotient property.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-70fbb087dae1e619c33b11a68104d6fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#49;&#125;&#125;&#123;&#92;&#115;&#113;&#114;&#116;&#123;&#54;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"26\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify the square root of 64. The numerator cannot be simplified.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d7d8ac2adb35e63ca1f9a7ce3974083a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#49;&#125;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"26\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596440488\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594160279\" data-type=\"problem\">\n<p id=\"fs-id1169594160281\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b9c53a65d4fca92431e345b510a3cd09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#57;&#125;&#123;&#52;&#57;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"35\" style=\"vertical-align: -11px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596394531\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596394533\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4c17f2c3f5bf15dbe5edd3c21b01bfab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#57;&#125;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"26\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596540574\" data-type=\"problem\">\n<p id=\"fs-id1169596540577\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-025e58e640c38b4456bb8b1a83fad78a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#56;&#125;&#123;&#56;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"35\" style=\"vertical-align: -11px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596589934\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596589936\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9ab92ed6949e82c78672e92785dfa8cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#92;&#115;&#113;&#114;&#116;&#123;&#55;&#125;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"26\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596641239\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596540572\" data-type=\"exercise\">\n<div id=\"fs-id1169596589934\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"title\">How to Use the Quotient Property to Simplify a Square Root<\/div>\n<div id=\"fs-id1169594012111\" data-type=\"exercise\">\n<div id=\"fs-id1169596648392\" data-type=\"problem\">\n<p id=\"fs-id1169596648394\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9ba4e9ca1c3298046197f5528cb2d81a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#55;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#49;&#57;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"54\" style=\"vertical-align: -11px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596625666\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p><span id=\"fs-id1169596557582\" data-type=\"media\" data-alt=\"This table has three columns and three rows. The first row reads, \u201cStep 1. Simplify the fraction in the radicand, if possible.\u201d Then it shows that 27 m cubed over 196 cannot be simplified. Then it shows the square root of 27 m cubed over 196.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_09_02_002a_img_new.jpg\" alt=\"This table has three columns and three rows. The first row reads, \u201cStep 1. Simplify the fraction in the radicand, if possible.\u201d Then it shows that 27 m cubed over 196 cannot be simplified. Then it shows the square root of 27 m cubed over 196.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169596764915\" data-type=\"media\" data-alt=\"The second row says, \u201cStep 2. Use the Quotient Property to rewrite the radical as the quotient of two radicals.\u201d Then it says, \u201cWe rewrite the square root of 27 m cubed over 196 as the quotient of the square root of 27 m cubed and the square root of 196.\u201d Then it shows the square root of 27 m cubed over the square root of 196.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_09_02_002b_img_new.jpg\" alt=\"The second row says, \u201cStep 2. Use the Quotient Property to rewrite the radical as the quotient of two radicals.\u201d Then it says, \u201cWe rewrite the square root of 27 m cubed over 196 as the quotient of the square root of 27 m cubed and the square root of 196.\u201d Then it shows the square root of 27 m cubed over the square root of 196.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1169596382516\" data-type=\"media\" data-alt=\"The third row says, \u201cStep 3. Simplify the radicals in the numerator and the denominator.\u201d Then it says, \u201c9 m squared and 196 are perfect squares.\u201d It then shows the square root of 9 m squared time the square root of 3 m over the square root of 196. It then shows 3 m times the square root of 3 m over 14.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_ElemAlg_Figure_09_02_002c_img_new.jpg\" alt=\"The third row says, \u201cStep 3. Simplify the radicals in the numerator and the denominator.\u201d Then it says, \u201c9 m squared and 196 are perfect squares.\u201d It then shows the square root of 9 m squared time the square root of 3 m over the square root of 196. It then shows 3 m times the square root of 3 m over 14.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596686530\" data-type=\"problem\">\n<p id=\"fs-id1169596686533\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-68ec310ade852361b1df1e9e7b0a6394_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#52;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#52;&#57;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"49\" style=\"vertical-align: -10px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594210515\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169594210517\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0d78b111e6cadd1d7ba1ab64271cc1c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#112;&#92;&#115;&#113;&#114;&#116;&#123;&#54;&#112;&#125;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"40\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596449674\" data-type=\"problem\">\n<p id=\"fs-id1169596449676\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-66d588887fecf2fff9567303529c9ba7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#56;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#49;&#48;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"50\" style=\"vertical-align: -11px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596308760\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596518525\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e9faa0215d36751066d8a029009b120b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#120;&#125;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"48\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">HOW TO: Simplify a square root using the quotient property.<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1169594175504\" class=\"stepwise\" type=\"1\">\n<li>Simplify the fraction in the radicand, if possible.<\/li>\n<li>Use the Quotient Property to rewrite the radical as the quotient of two radicals.<\/li>\n<li>Simplify the radicals in the numerator and the denominator.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596587259\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596686528\" data-type=\"exercise\">\n<div id=\"fs-id1169596686530\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596686008\" data-type=\"problem\">\n<p id=\"fs-id1169596239293\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c06b8d2edf0654cdd80369c9063f309_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#53;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"50\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594167750\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c06b8d2edf0654cdd80369c9063f309_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#53;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"50\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">We cannot simplify the fraction in the radicand. Rewrite using the Quotient Property.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f90454723281abfe7ee09152195e44da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#115;&#113;&#114;&#116;&#123;&#52;&#53;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#125;&#125;&#123;&#92;&#115;&#113;&#114;&#116;&#123;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"40\" style=\"vertical-align: -15px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify the radicals in the numerator and the denominator.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e9f4f0e403f8f30e79eef1e04f957617_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#115;&#113;&#114;&#116;&#123;&#57;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#120;&#125;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"63\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-729a4bd7b77d46789dfd3708c08047ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#120;&#125;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"48\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594171172\" data-type=\"problem\">\n<p id=\"fs-id1169594171174\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8e7abe0f3ef694fc9169a4e9428695a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#48;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#123;&#110;&#125;&#94;&#123;&#54;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"54\" style=\"vertical-align: -11px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596626003\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596598359\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-158148208de94abd020195ea3c78817b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#109;&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#109;&#125;&#125;&#123;&#123;&#110;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"50\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596704774\" data-type=\"problem\">\n<p id=\"fs-id1169594159672\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d04661a58ff25bf4758d590295c66ba7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#52;&#123;&#117;&#125;&#94;&#123;&#55;&#125;&#125;&#123;&#123;&#118;&#125;&#94;&#123;&#56;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"50\" style=\"vertical-align: -11px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596522185\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596522188\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8acdf9028eea88658febcc0a29a65d19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#123;&#117;&#125;&#94;&#123;&#51;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#54;&#117;&#125;&#125;&#123;&#123;&#118;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"48\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169594014279\">Be sure to simplify the fraction in the radicand first, if possible.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594212440\" data-type=\"problem\">\n<p id=\"fs-id1169594154637\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1874e948e50d13491e1cf5c2a389e937_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#49;&#123;&#100;&#125;&#94;&#123;&#57;&#125;&#125;&#123;&#50;&#53;&#123;&#100;&#125;&#94;&#123;&#52;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"49\" style=\"vertical-align: -11px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596517992\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1874e948e50d13491e1cf5c2a389e937_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#49;&#123;&#100;&#125;&#94;&#123;&#57;&#125;&#125;&#123;&#50;&#53;&#123;&#100;&#125;&#94;&#123;&#52;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"49\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify the fraction in the radicand.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1a74180dfd253431473acae5297a3e81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#49;&#123;&#100;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#50;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"49\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite using the Quotient Property.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-27353969821a379ad340258f1b2bdd54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#115;&#113;&#114;&#116;&#123;&#56;&#49;&#123;&#100;&#125;&#94;&#123;&#53;&#125;&#125;&#125;&#123;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"31\" width=\"40\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify the radicals in the numerator and the denominator.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2084a6c16bb35d210d44642441f335fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#115;&#113;&#114;&#116;&#123;&#56;&#49;&#123;&#100;&#125;&#94;&#123;&#52;&#125;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#115;&#113;&#114;&#116;&#123;&#100;&#125;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"62\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a2d10c33987cbfc97425da006ccef40f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#123;&#100;&#125;&#94;&#123;&#50;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#100;&#125;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"40\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594011369\" data-type=\"problem\">\n<p id=\"fs-id1169594011371\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6bba3a2217106332d24ba709d55e1ec4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#52;&#123;&#120;&#125;&#94;&#123;&#55;&#125;&#125;&#123;&#57;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"50\" style=\"vertical-align: -11px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594123346\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169594051361\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dd7e54c59bc412bdd05614195134762a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"22\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596446742\" data-type=\"problem\">\n<p id=\"fs-id1169596446744\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-33e27402f0b319322f9649c021ef6e4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#54;&#123;&#97;&#125;&#94;&#123;&#57;&#125;&#125;&#123;&#49;&#48;&#48;&#123;&#97;&#125;&#94;&#123;&#53;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"56\" style=\"vertical-align: -11px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594101856\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169594101859\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d6e811b2cf371b8316c561148bba9cad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"21\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594050085\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594011367\" data-type=\"exercise\">\n<div id=\"fs-id1169594011369\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 17<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596447985\" data-type=\"problem\">\n<p id=\"fs-id1169596447987\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7dfa981c24b36503abff2f8f6ff6cdb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#56;&#123;&#112;&#125;&#94;&#123;&#53;&#125;&#123;&#113;&#125;&#94;&#123;&#55;&#125;&#125;&#123;&#51;&#50;&#112;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"62\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594063563\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7dfa981c24b36503abff2f8f6ff6cdb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#56;&#123;&#112;&#125;&#94;&#123;&#53;&#125;&#123;&#113;&#125;&#94;&#123;&#55;&#125;&#125;&#123;&#51;&#50;&#112;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"62\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify the fraction in the radicand, if possible.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0688ac82521d87140175ec7c3031bb15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#123;&#112;&#125;&#94;&#123;&#52;&#125;&#123;&#113;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#49;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"55\" style=\"vertical-align: -9px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Rewrite using the Quotient Property.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-793c31132f90502d676a7701c6503041_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#115;&#113;&#114;&#116;&#123;&#57;&#123;&#112;&#125;&#94;&#123;&#52;&#125;&#123;&#113;&#125;&#94;&#123;&#53;&#125;&#125;&#125;&#123;&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"49\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify the radicals in the numerator and the denominator.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-48007ad4c58e862f4b62e3084cf24935_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#115;&#113;&#114;&#116;&#123;&#57;&#123;&#112;&#125;&#94;&#123;&#52;&#125;&#123;&#113;&#125;&#94;&#123;&#52;&#125;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#115;&#113;&#114;&#116;&#123;&#113;&#125;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"71\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">Simplify.<\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4d1c4cfcdae4430f3cb18ead05ed7537_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#113;&#125;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"52\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 17.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594206609\" data-type=\"problem\">\n<p id=\"fs-id1169596704334\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-49b8001371821422a454f55897df1efd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#48;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#55;&#50;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#121;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"64\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596765965\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596765967\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-acb0358ee4e49ab8719bdda66be7a762_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#121;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#125;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"34\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 17.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596244116\" data-type=\"problem\">\n<p id=\"fs-id1169596244118\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f599e59e83a0bcde88e95d65e4e0be7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#56;&#123;&#109;&#125;&#94;&#123;&#55;&#125;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#49;&#50;&#53;&#123;&#109;&#125;&#94;&#123;&#53;&#125;&#123;&#110;&#125;&#94;&#123;&#57;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"76\" style=\"vertical-align: -11px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594004728\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169594004731\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cb052ba4e6cfa53d8f65e6d772637b02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#109;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#125;&#125;&#123;&#53;&#123;&#110;&#125;&#94;&#123;&#51;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#110;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"49\" style=\"vertical-align: -11px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1169594002164\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">Simplified Square Root<\/strong><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fc3feabd59870f8b605474392224184c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"24\" style=\"vertical-align: -4px;\" \/> is considered simplified if <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> has no perfect-square factors.<\/li>\n<li><strong data-effect=\"bold\">Product Property of Square Roots<\/strong> If <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em> are non-negative real numbers, then\n<div id=\"fs-id1169594148789\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6ff242883a3900afc247a1a5f1d120ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#97;&#98;&#125;&#61;&#92;&#115;&#113;&#114;&#116;&#123;&#97;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#115;&#113;&#114;&#116;&#123;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"114\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/li>\n<li><strong data-effect=\"bold\">Simplify a Square Root Using the Product Property<\/strong> To simplify a square root using the Product Property:\n<ol id=\"fs-id1169594079028\" class=\"stepwise\" type=\"1\">\n<li>Find the largest perfect square factor of the radicand. Rewrite the radicand as a product using the perfect square factor.<\/li>\n<li>Use the product rule to rewrite the radical as the product of two radicals.<\/li>\n<li>Simplify the square root of the perfect square.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">Quotient Property of Square Roots<\/strong> If <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em> are non-negative real numbers and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1edd53778d94abb1dc1e19acff79e9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"40\" style=\"vertical-align: -4px;\" \/>, then\n<div id=\"fs-id1169596380046\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-eb22982ecd74816acc96edd972c29616_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#115;&#113;&#114;&#116;&#123;&#97;&#125;&#125;&#123;&#92;&#115;&#113;&#114;&#116;&#123;&#98;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"73\" style=\"vertical-align: -11px;\" \/><\/div>\n<\/li>\n<li><strong data-effect=\"bold\">Simplify a Square Root Using the Quotient Property<\/strong> To simplify a square root using the Quotient Property:\n<ol id=\"fs-id1169594102064\" class=\"stepwise\" type=\"1\">\n<li>Simplify the fraction in the radicand, if possible.<\/li>\n<li>Use the Quotient Rule to rewrite the radical as the quotient of two radicals.<\/li>\n<li>Simplify the radicals in the numerator and the denominator.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1>Practice Makes Perfect<\/h1>\n<h2 id=\"fs-id1169594011876\">Use the Product Property to Simplify Square Roots<\/h2>\n<p id=\"fs-id1168741952304\">In the following exercises, simplify.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 378px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">1. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a2a360f51ae982fb29f5e4206b8fd133_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"32\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">2. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8245719f6677d6deec8098239687ab7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#56;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"32\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">3. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-904be03cc4596bd2b7eb61de366bd7af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">4. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-619e33f0d425102d677cf9d553fdb378_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#57;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"32\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5d721d31489db78a6cecd84196de173e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">6. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dd72d8f0415a7de7de8e2098aa523a4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#52;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7db8632715a7bad66865e3607d10fca4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#52;&#53;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">8. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5a1c842b75e20013322e2715a2979798_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#53;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-85b3c5447a924986a71e55e0dfbf4ed8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#56;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">10. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a642ba7178048ea82da606df087636e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#56;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cc126a0a9ff55fd169cf1d890f7b822a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#54;&#55;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">12. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-999500a1024889ea9072dc7d1168d7e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#50;&#53;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"50\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3435d67e20db3e4b45ce4a762ca69b76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#123;&#120;&#125;&#94;&#123;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"32\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">14. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3729fc682fe989f83bed25e71e3e857d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#123;&#121;&#125;&#94;&#123;&#49;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"41\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-499a1df6bcdac45f9bd2129c52a12c4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"34\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">16. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8660cfbfe2b3765bad083c857e596502_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#123;&#113;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"34\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7c684d36bf5b97e8abea5e2040b97443_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#123;&#109;&#125;&#94;&#123;&#49;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">18. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5d2ff3b351499e361aaab59b216c0e8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#123;&#110;&#125;&#94;&#123;&#50;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"40\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f2fc31564d57b3b3c00be61d8eedf6b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#123;&#114;&#125;&#94;&#123;&#50;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">20. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f1fd03041f06b7f99b25cd28733bff45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#123;&#115;&#125;&#94;&#123;&#51;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"37\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2932bb3da4c04e86f944be119a46ece0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#52;&#57;&#123;&#110;&#125;&#94;&#123;&#49;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"57\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">22. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bb13290798c6cfa0a101cc9dd01fa5a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#53;&#123;&#109;&#125;&#94;&#123;&#57;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"55\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-85ec07ed8e3ac2004efc55d28399673a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#56;&#49;&#123;&#114;&#125;&#94;&#123;&#49;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"55\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">24. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f24fda584a1d02658859a0b4c8e9413a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#48;&#48;&#123;&#115;&#125;&#94;&#123;&#49;&#57;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"64\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ef8367b9e7db0f0ccba80074c5fccd65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#57;&#56;&#123;&#109;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"55\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0b9e179fcb24b1e6f07f87568fd4b359_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#50;&#123;&#110;&#125;&#94;&#123;&#49;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"57\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-63a60fb0244a619ad616513afd9f4c43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#50;&#53;&#123;&#114;&#125;&#94;&#123;&#49;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"64\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">28. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3567bb32f28de0ac97d87c51925883f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#56;&#48;&#123;&#115;&#125;&#94;&#123;&#49;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"55\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-74242f867433f7de0d81faa3968b4d2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#48;&#48;&#123;&#112;&#125;&#94;&#123;&#49;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"68\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">30. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a6f0ef597cae051c32b466973aea4860_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#50;&#56;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1c40ba6eeb566cb088cf2cac2805dd01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#52;&#50;&#123;&#109;&#125;&#94;&#123;&#50;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"71\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">32. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4fcf5936f8caf00f7287843fe02d227c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#55;&#53;&#123;&#110;&#125;&#94;&#123;&#49;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-04eb54576aa7a88ccdf96f01a6fb9e71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#52;&#55;&#123;&#109;&#125;&#94;&#123;&#55;&#125;&#123;&#110;&#125;&#94;&#123;&#49;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"90\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">34. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-db58b65ddd1aea72741e3339846d7da0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#52;&#56;&#123;&#109;&#125;&#94;&#123;&#55;&#125;&#123;&#110;&#125;&#94;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"74\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">35.<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-37cc88763a9f3145d13648c9fedf77b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#55;&#53;&#123;&#114;&#125;&#94;&#123;&#49;&#51;&#125;&#123;&#115;&#125;&#94;&#123;&#57;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"71\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">36. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-37398429e9a771e69324cd1113e90e20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#57;&#54;&#123;&#114;&#125;&#94;&#123;&#51;&#125;&#123;&#115;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"64\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dd55799b70fcb6aef300dd15101ef18d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#48;&#48;&#123;&#112;&#125;&#94;&#123;&#57;&#125;&#123;&#113;&#125;&#94;&#123;&#49;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">38. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3ca80f3f3f03fa182807c90156b2a83b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#57;&#50;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#123;&#114;&#125;&#94;&#123;&#55;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"77\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0a42f432e5c2e98664f2f943c6cc5094_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#52;&#50;&#123;&#109;&#125;&#94;&#123;&#49;&#51;&#125;&#123;&#110;&#125;&#94;&#123;&#50;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"96\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">40. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cea02678c0ff28fc808c0b13ab34d897_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#53;&#48;&#123;&#109;&#125;&#94;&#123;&#57;&#125;&#123;&#110;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"83\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">41. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-177331e3c6322d9476b9cbd544623252_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#43;&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">42. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-90a5d4001c30a750c46d98f55a397fa2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#43;&#92;&#115;&#113;&#114;&#116;&#123;&#57;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9797f5ebaaff2e87870867be513bc1a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#43;&#92;&#115;&#113;&#114;&#116;&#123;&#52;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"62\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">44. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b870121203e16a648b6e8ee5499f34c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#43;&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"72\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3747b56e6e5e267f71e782d1e408aa87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#45;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#52;&#125;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"50\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">46. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-39e660ca6df5e41f684c74201211d589_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#45;&#92;&#115;&#113;&#114;&#116;&#123;&#56;&#48;&#125;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"43\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e3595f5832712c22aea68eacf348357c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#43;&#92;&#115;&#113;&#114;&#116;&#123;&#57;&#48;&#125;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"43\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">48. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4eac9d6a2e2e739f5bfe8b6425b593b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#53;&#43;&#92;&#115;&#113;&#114;&#116;&#123;&#55;&#53;&#125;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"50\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169594059546\"><strong data-effect=\"bold\"><br \/>\n<\/strong>Use the Quotient Property to Simplify Square Roots<\/h2>\n<p id=\"fs-id1168745119026\">In the following exercises, simplify.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 294px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-061385e9cdea2850bfff22ad260c64a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#57;&#125;&#123;&#54;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"35\" style=\"vertical-align: -11px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">50. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1a90dad6cd56fc829fe78c38ada5d178_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#48;&#125;&#123;&#51;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"42\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0780d166a4c84a9551bff126d0254d15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#50;&#49;&#125;&#123;&#49;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"42\" style=\"vertical-align: -11px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">52. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8e680b577aabd921ee86a28e309c1ae5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#52;&#52;&#125;&#123;&#49;&#54;&#57;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"42\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-580dd1d4ee4ef6f6f33b5dae8b547d56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#50;&#125;&#123;&#57;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"35\" style=\"vertical-align: -11px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">54. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aba0c93ef6275c6a747afd1c0e16cbe5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#53;&#125;&#123;&#49;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"35\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1be45da32285081ae7b597dd8510abbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#50;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"35\" style=\"vertical-align: -10px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">56. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5d7c5155a2c89242d75654caa9b2029b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#48;&#48;&#125;&#123;&#50;&#52;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"42\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">57. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f424cde74112429a46a4040a828d7dce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#120;&#125;&#94;&#123;&#49;&#48;&#125;&#125;&#123;&#123;&#120;&#125;&#94;&#123;&#54;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"42\" style=\"vertical-align: -11px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">58. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-422222a450630e927c7ded5691b3caea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#112;&#125;&#94;&#123;&#50;&#48;&#125;&#125;&#123;&#123;&#112;&#125;&#94;&#123;&#49;&#48;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"41\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">59. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-12fc15f2f6d9ee38d5c635f7ae4e7efa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#56;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"35\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">60. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b073a621e06a1ce1c54c011abe20e5be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#113;&#125;&#94;&#123;&#56;&#125;&#125;&#123;&#123;&#113;&#125;&#94;&#123;&#49;&#52;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"41\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-432e70791092c82c032eb121b830f8a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#48;&#48;&#123;&#120;&#125;&#94;&#123;&#55;&#125;&#125;&#123;&#50;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"57\" style=\"vertical-align: -11px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">62. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3b02178485b87484c8e56c8a5a126003_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#56;&#123;&#121;&#125;&#94;&#123;&#49;&#49;&#125;&#125;&#123;&#50;&#123;&#121;&#125;&#94;&#123;&#53;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"55\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bdfece3a154587705c57995dbb8579bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#54;&#123;&#112;&#125;&#94;&#123;&#57;&#125;&#125;&#123;&#54;&#112;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"49\" style=\"vertical-align: -11px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">64. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9c8ed13817ac171af7d765be781ea822_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#56;&#123;&#113;&#125;&#94;&#123;&#49;&#48;&#125;&#125;&#123;&#51;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"61\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">65. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4de3f90732be2d9001c4cc0f39fd47e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#54;&#125;&#123;&#51;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"35\" style=\"vertical-align: -11px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">66. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-40613c205161c01a98016fc24cb6edaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#52;&#52;&#125;&#123;&#54;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"42\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">67. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e9f90b375f3f1d202d4030be0276668_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#48;&#125;&#123;&#56;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"35\" style=\"vertical-align: -11px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">68. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ce0c8f3fd06dbe8cbd10120596c19327_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#49;&#125;&#123;&#49;&#57;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"42\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">69. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cbc11eeef7ed9588a0088a6fd9a7d5ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#54;&#123;&#120;&#125;&#94;&#123;&#55;&#125;&#125;&#123;&#49;&#50;&#49;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"50\" style=\"vertical-align: -11px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">70. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b4941a30c6029d3ef653d99d6543e041_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#56;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#52;&#57;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"56\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">71. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5f29cde980680097ebb985d916c86298_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#48;&#48;&#123;&#109;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#54;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"61\" style=\"vertical-align: -11px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">72. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bb0979434bd490e1a2fd450791df24b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#50;&#53;&#123;&#110;&#125;&#94;&#123;&#55;&#125;&#125;&#123;&#49;&#54;&#57;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"57\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">73. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b4a8b2fe8aaaf7c6c040b96227d30860_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#56;&#123;&#114;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#49;&#48;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"48\" style=\"vertical-align: -11px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">74. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b6bbc29605ed2a97d5df8dcf2bae5e21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#56;&#48;&#123;&#115;&#125;&#94;&#123;&#49;&#48;&#125;&#125;&#123;&#49;&#52;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"61\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">75. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f82b0c96ea63ee957c0e6a7569041123_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#56;&#123;&#113;&#125;&#94;&#123;&#54;&#125;&#125;&#123;&#50;&#50;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"49\" style=\"vertical-align: -10px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">76. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f6b66e15a58b8adee331c9ce0be45a8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#53;&#48;&#123;&#114;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#50;&#53;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"55\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">77. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6b26276b416b81701c74617bfc57e7a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#53;&#123;&#114;&#125;&#94;&#123;&#57;&#125;&#125;&#123;&#123;&#115;&#125;&#94;&#123;&#56;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"48\" style=\"vertical-align: -11px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">78. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1c687622281f730c28054bfd38351cae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#50;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#54;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"50\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">79. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3fa03ec15d15b72c071ef89556419042_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#56;&#123;&#112;&#125;&#94;&#123;&#55;&#125;&#125;&#123;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"49\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">80. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6d7ef5f7bdc7386dc85f6c0c048807b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#53;&#123;&#114;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#123;&#115;&#125;&#94;&#123;&#49;&#48;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"48\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">81. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-650b010b96cd3e040e89d6b3ad7e614f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#48;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#51;&#54;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"57\" style=\"vertical-align: -11px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">82. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-84208ccbbf36ec26645ef90cef3cc7fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#57;&#123;&#114;&#125;&#94;&#123;&#49;&#50;&#125;&#125;&#123;&#49;&#54;&#123;&#114;&#125;&#94;&#123;&#54;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"54\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">83. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cd8918f49c978fdbc4f21fb437f4ee1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#50;&#49;&#123;&#112;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#56;&#49;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"56\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">84. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-15781a71b41d651265f9babd62bd4771_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#53;&#123;&#114;&#125;&#94;&#123;&#56;&#125;&#125;&#123;&#54;&#52;&#114;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"48\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">85. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-62adc49beb700c0713cf59d0f74ade9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#50;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#49;&#56;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#121;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"64\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">86. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-97e808822f6d3b7dd64abefd5fc9a820_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#53;&#123;&#114;&#125;&#94;&#123;&#54;&#125;&#123;&#115;&#125;&#94;&#123;&#56;&#125;&#125;&#123;&#52;&#56;&#114;&#123;&#115;&#125;&#94;&#123;&#52;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"62\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">87. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-31336a1cf2f06f788d9f3548b9a3f489_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#55;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#113;&#125;&#123;&#49;&#48;&#56;&#123;&#112;&#125;&#94;&#123;&#53;&#125;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"69\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 50%; height: 14px;\">88. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5e5fa8fe4767a26648a8194df4fcbb57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#48;&#123;&#114;&#125;&#94;&#123;&#53;&#125;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#49;&#50;&#56;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#123;&#115;&#125;&#94;&#123;&#53;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"68\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 data-type=\"title\">Everyday Math<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">89.<\/p>\n<p>a) Elliott decides to construct a square garden that will take up 288 square feet of his yard. Simplify <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a642ba7178048ea82da606df087636e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#56;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/> to determine the length and the width of his garden. Round to the nearest tenth of a foot.<\/p>\n<p>b) Suppose Elliott decides to reduce the size of his square garden so that he can create a 5-foot-wide walking path on the north and east sides of the garden. Simplify <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d4c032a652352af62c0d24a533db324b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#56;&#56;&#125;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"70\" style=\"vertical-align: -2px;\" \/> to determine the length and width of the new garden. Round to the nearest tenth of a foot.<\/td>\n<td style=\"width: 50%;\">90.<\/p>\n<p>a) Melissa accidentally drops a pair of sunglasses from the top of a roller coaster, 64 feet above the ground. Simplify <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9fefa28752520ab89caf5e37d8cb7c9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#52;&#125;&#123;&#49;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"35\" style=\"vertical-align: -11px;\" \/> to determine the number of seconds it takes for the sunglasses to reach the ground.<\/p>\n<p>b) Suppose the sunglasses in the previous example were dropped from a height of 144 feet. Simplify <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-385b30e7f64fe78b4f16ffbb015025a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#52;&#52;&#125;&#123;&#49;&#54;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"42\" style=\"vertical-align: -11px;\" \/> to determine the number of seconds it takes for the sunglasses to reach the ground.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 data-type=\"title\">Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">91. Explain why <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5d158ff4c23466078312b92608e505f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#125;&#61;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"72\" style=\"vertical-align: -1px;\" \/>. Then explain why <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4e527368455b5c80532202f5d27bb060_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#123;&#120;&#125;&#94;&#123;&#49;&#54;&#125;&#125;&#61;&#123;&#120;&#125;&#94;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"79\" style=\"vertical-align: -1px;\" \/>.<\/td>\n<td style=\"width: 50%;\">92. Explain why <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f0dd07f51f1fa9ddf0fd88a132170de1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#43;&#92;&#115;&#113;&#114;&#116;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"54\" style=\"vertical-align: -2px;\" \/> is not equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8934cf61cdc67882f01dfba6542ed4a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#115;&#113;&#114;&#116;&#123;&#55;&#43;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"54\" style=\"vertical-align: -3px;\" \/>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%; height: 208px;\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">1. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6ea061df92a4307f25647a6421a3a708_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"33\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">3. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6d7a9343e2a2f74aa72f3278cbb70ff7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"33\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-487f517ca901f87c531a4f1f2ca68317_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8aa005121b316d3d4c9041822db820fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-06d59cff23b8dbedd41703f35733e78a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"42\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7ff0eaf362ac2a8cdacaca43fb2c98e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"41\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b0f8480814e4ab3456a1eb1bca14f876_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"44\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dfe68f98fa11b97e5b6dfc8b18a578b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#92;&#115;&#113;&#114;&#116;&#123;&#112;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"34\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fadac40b15bb3e59fd0198c843c19164_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#54;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"54\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ef15271049d75af2e953b269b3b23939_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#114;&#125;&#94;&#123;&#49;&#50;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"47\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-567eea31e840db76bea80ef7976260b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#123;&#110;&#125;&#94;&#123;&#56;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"53\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f22e1744ea9d5153164bfd1702c7a14c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#123;&#114;&#125;&#94;&#123;&#55;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"49\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-012c0ee9cb744657c381f64a1ff48160_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"72\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d13599c6d516d245952b982dd807374a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#114;&#125;&#94;&#123;&#54;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"58\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9f38bf1d7246fe533ffcef2e7424f841_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#123;&#112;&#125;&#94;&#123;&#54;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#112;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0d0bf03fba5a698e37f2050e78afc6f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#123;&#109;&#125;&#94;&#123;&#49;&#49;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"87\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e5b93ff95e983d0bcf3204621a771196_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#123;&#110;&#125;&#94;&#123;&#53;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#109;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"101\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-697f8de06bd88373de929e928c3ba848_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#114;&#125;&#94;&#123;&#54;&#125;&#123;&#115;&#125;&#94;&#123;&#52;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#114;&#115;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"82\" style=\"vertical-align: -2px;\" \/> 70)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5ab00593748af59502e7629415d26629_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#123;&#112;&#125;&#94;&#123;&#52;&#125;&#123;&#113;&#125;&#94;&#123;&#53;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#112;&#113;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ee024257f38f684a25fbcd72a19ee94b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#123;&#109;&#125;&#94;&#123;&#54;&#125;&#123;&#110;&#125;&#94;&#123;&#49;&#48;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#109;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"116\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">41. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-32736d1d9a81d5e19f611f03617e5b29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#43;&#50;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-edcd66b0fafd82a283dcc70075d37030_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#43;&#51;&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"62\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-72456a180c00bba4c19ce10b1732425a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#45;&#50;&#92;&#115;&#113;&#114;&#116;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"63\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-83f01d14929ee661da4551f55710f995_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#43;&#92;&#115;&#113;&#114;&#116;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"62\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-27a06edc5fe1932bd0c3274d9af93920_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5b68294c2a73f2ea0d02861b81ab877d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3f02bad88e2a55c2a7c2d7b601e31c79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-56fd13ae94393ab95b21e4d3651f1ec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">57. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b40448f90dbf1bf9cce1035e2f3b1120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">59. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d9c43903db1769a723d4e4e4599a19f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"15\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-545896568f3fc11d87491c9694a5067c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"34\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-008eaecf175a81356fab67d5f7cf0e9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#112;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"25\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">65. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3d82dcd9f5ceb6abe3be82cbafbf119b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"26\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">67. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-18c2e4eb29595bc65908a0b3cf55f7c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#92;&#115;&#113;&#114;&#116;&#123;&#53;&#125;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"26\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">69. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cf8729a5d48ed2c71b598f8212c7b0ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#54;&#120;&#125;&#125;&#123;&#49;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"48\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">71. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-718a736d465fff22c0b55174271157e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#109;&#125;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"64\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">73. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6301cf1971d5ecd5052d4973de475845_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#50;&#114;&#125;&#125;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"46\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">75. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-31f2ef12bab34e2f753d8c56b8eae709_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#55;&#125;&#125;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"39\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 16px;\">77. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d49e024270f63339ff61cf2451f0aaa6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#123;&#114;&#125;&#94;&#123;&#52;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#51;&#114;&#125;&#125;&#123;&#123;&#115;&#125;&#94;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"46\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">79. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aa8deacd7d5c66d0145fb00dbce5094a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#92;&#115;&#113;&#114;&#116;&#123;&#55;&#112;&#125;&#125;&#123;&#113;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"46\" style=\"vertical-align: -9px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">81. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-da8db69e3f2434072cc80c5016c8710e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#120;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"15\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">83. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d5f3685f278c34bb9739cff43b20753a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#112;&#92;&#115;&#113;&#114;&#116;&#123;&#112;&#125;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"40\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">85. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cca138ab6ac2290b744e657c3ff9b9ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#120;&#121;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"22\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">87. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-37d7ea763ea8607bf1a80235f314862c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#112;&#113;&#92;&#115;&#113;&#114;&#116;&#123;&#112;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"39\" style=\"vertical-align: -11px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">89. a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c32321c8a8e9f43c732683ae95485bf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;&#46;&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#101;&#101;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"61\" style=\"vertical-align: -1px;\" \/>b)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8cbfaab930a8a13319582a8511675877_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#46;&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#101;&#101;&#116;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"61\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">91.\u00a0Answers will vary.<\/td>\n<td style=\"width: 33.3333%;\"><\/td>\n<td style=\"width: 33.3333%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cSimplify Square Roots\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<!-- pb_fixme --><\/p>\n","protected":false},"author":90,"menu_order":5,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2011","chapter","type-chapter","status-publish","hentry"],"part":1897,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/2011","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":2,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/2011\/revisions"}],"predecessor-version":[{"id":2526,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/2011\/revisions\/2526"}],"part":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/parts\/1897"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/2011\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/media?parent=2011"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=2011"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/contributor?post=2011"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/license?post=2011"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}