{"id":1960,"date":"2021-12-02T19:40:12","date_gmt":"2021-12-03T00:40:12","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-9-4\/"},"modified":"2023-09-01T14:40:19","modified_gmt":"2023-09-01T18:40:19","slug":"answer-key-9-4","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-9-4\/","title":{"raw":"Answer Key 9.4","rendered":"Answer Key 9.4"},"content":{"raw":"
    \r\n \t
  1. [latex]12\\sqrt{5\\cdot 16}[\/latex]\r\n[latex]12\\cdot 4 \\sqrt{5}[\/latex]\r\n[latex]48\\sqrt{5}[\/latex]<\/li>\r\n \t
  2. [latex]-5\\sqrt{10\\cdot 15}[\/latex]\r\n[latex]-5\\sqrt{150}[\/latex]\r\n[latex]-5\\sqrt{25\\cdot 6}\\Rightarrow -25\\sqrt{6}[\/latex]<\/li>\r\n \t
  3. [latex]\\sqrt{15\\cdot 12\\cdot m^2}[\/latex]\r\n[latex]\\sqrt{3\\cdot 5\\cdot 3\\cdot 4\\cdot m^2}[\/latex]\r\n[latex]3\\cdot 2m\\sqrt{5}[\/latex]\r\n[latex]6m\\sqrt{5}[\/latex]<\/li>\r\n \t
  4. [latex]-5\\sqrt{5r^3\\cdot 10r^2}[\/latex]\r\n[latex]-5\\sqrt{25\\cdot 2\\cdot r^4\\cdot r}[\/latex]\r\n[latex]-25r^2\\sqrt{2r}[\/latex]<\/li>\r\n \t
  5. [latex]\\sqrt[3]{8x^7}[\/latex]\r\n[latex]\\sqrt[3]{8\\cdot x^6\\cdot x}[\/latex]\r\n[latex]2x^2 \\sqrt[3]{x}[\/latex]<\/li>\r\n \t
  6. [latex]3 \\sqrt[3]{40a^7}[\/latex]\r\n[latex]3 \\sqrt[3]{5\\cdot 8\\cdot a^6\\cdot a}[\/latex]\r\n[latex]3\\cdot 2a^2 \\sqrt[3]{5a}\\Rightarrow 6a^2 \\sqrt[3]{5a}[\/latex]<\/li>\r\n \t
  7. [latex]\\sqrt{12}+2\\sqrt{6}[\/latex]\r\n[latex]\\sqrt{4\\cdot 3}+2\\sqrt{6}[\/latex]\r\n[latex]2\\sqrt{3}+2\\sqrt{6}[\/latex]<\/li>\r\n \t
  8. [latex]\\sqrt{50}+\\sqrt{20}[\/latex]\r\n[latex]\\sqrt{25\\cdot 2}+\\sqrt{4\\cdot 5}[\/latex]\r\n[latex]5\\sqrt{2}+2\\sqrt{5}[\/latex]<\/li>\r\n \t
  9. [latex]-15\\sqrt{45}-10\\sqrt{15}[\/latex]\r\n[latex]-15\\sqrt{9\\cdot 5}-10\\sqrt{15}[\/latex]\r\n[latex]-15\\cdot 3\\sqrt{5}-10\\sqrt{15}[\/latex]\r\n[latex]-45\\sqrt{5}-10\\sqrt{15}[\/latex]<\/li>\r\n \t
  10. [latex]15\\sqrt{45}+10\\sqrt{15}[\/latex]\r\n[latex]15\\sqrt{9\\cdot 5}+10\\sqrt{15}[\/latex]\r\n[latex]15\\cdot 3\\sqrt{5}+10\\sqrt{15}[\/latex]\r\n[latex]45\\sqrt{5}+10\\sqrt{15}[\/latex]<\/li>\r\n \t
  11. [latex]25n\\sqrt{10}+5\\sqrt{20}[\/latex]\r\n[latex]25n\\sqrt{10}+5\\sqrt{4\\cdot 5}[\/latex]\r\n[latex]25n\\sqrt{10}+10\\sqrt{5}[\/latex]<\/li>\r\n \t
  12. [latex]\\sqrt{75}-3\\sqrt{45v}[\/latex]\r\n[latex]\\sqrt{25\\cdot 3}-3\\sqrt{9\\cdot 5v}[\/latex]\r\n[latex]5\\sqrt{3}-9\\sqrt{5v}[\/latex]<\/li>\r\n \t
  13. [latex]-6+2\\sqrt{2}-6\\sqrt{2}+2(\\sqrt{2})(\\sqrt{2})[\/latex]\r\n[latex]-6+2\\sqrt{2}-6\\sqrt{2}+2(2)[\/latex]\r\n[latex]-6+4+2\\sqrt{2}-6\\sqrt{2}[\/latex]\r\n[latex]-2-4\\sqrt{2}[\/latex]<\/li>\r\n \t
  14. [latex]10-4\\sqrt{3}-5\\sqrt{3}+2(\\sqrt{3})(\\sqrt{3})[\/latex]\r\n[latex]10-4\\sqrt{3}-5\\sqrt{3}+2(3)[\/latex]\r\n[latex]10+6-4\\sqrt{3}-5\\sqrt{3}[\/latex]\r\n[latex]16-9\\sqrt{3}[\/latex]<\/li>\r\n \t
  15. [latex](2\\sqrt{5})(\\sqrt{5})-\\sqrt{5}-10\\sqrt{5}+5[\/latex]\r\n[latex]2(5)-\\sqrt{5}-10\\sqrt{5}+5[\/latex]\r\n[latex]10+5-\\sqrt{5}-10\\sqrt{5}[\/latex]\r\n[latex]15-11\\sqrt{5}[\/latex]<\/li>\r\n \t
  16. [latex]10(3)+4\\sqrt{12}+5\\sqrt{15}+2\\sqrt{20}[\/latex]\r\n[latex]30+4\\sqrt{4\\cdot 3}+5\\sqrt{15}+2\\sqrt{5\\cdot 4}[\/latex]\r\n[latex]30+5\\sqrt{15}+8\\sqrt{3}+4\\sqrt{5}[\/latex]<\/li>\r\n \t
  17. [latex]3(2a)+6\\sqrt{6a^2}+\\sqrt{10a^2}+2\\sqrt{15a^2}[\/latex]\r\n[latex]6a+6a\\sqrt{6}+a\\sqrt{10}+2a\\sqrt{15}[\/latex]<\/li>\r\n \t
  18. [latex](-2\\sqrt{2p}+5\\sqrt{5})(2\\sqrt{5p})[\/latex]\r\n[latex]-4\\sqrt{10p^2}+10\\sqrt{25p}[\/latex]\r\n[latex]-4p\\sqrt{10}+50\\sqrt{p}[\/latex]<\/li>\r\n \t
  19. [latex]15+12\\sqrt{3}+20\\sqrt{3}+16(3)[\/latex]\r\n[latex]63+32\\sqrt{3}[\/latex]<\/li>\r\n \t
  20. [latex]-5\\sqrt{4m}+\\sqrt{2m}+25\\sqrt{2}-5[\/latex]\r\n[latex]-10\\sqrt{m}+\\sqrt{2m}+25\\sqrt{2}-5[\/latex]<\/li>\r\n \t
  21. [latex]\\dfrac{\\sqrt{12}}{5\\sqrt{100}}\\div \\sqrt{4}[\/latex]\r\n[latex]\\phantom{a}[\/latex]\r\n[latex]\\dfrac{\\sqrt{3}}{5\\sqrt{25}}\\Rightarrow \\dfrac{\\sqrt{3}}{5\\cdot 5}\\Rightarrow \\dfrac{\\sqrt{3}}{25}[\/latex]<\/li>\r\n \t
  22. [latex]\\dfrac{\\sqrt{15}}{2\\cdot 2}\\Rightarrow \\dfrac{\\sqrt{15}}{4}[\/latex]<\/li>\r\n \t
  23. [latex]\\dfrac{\\sqrt{5}}{4\\sqrt{125}}\\div \\sqrt{5}[\/latex]\r\n[latex]\\phantom{a}[\/latex]\r\n[latex]\\dfrac{\\sqrt{1}}{4\\sqrt{25}}\\Rightarrow \\dfrac{1}{4\\cdot 5}\\Rightarrow \\dfrac{1}{20}[\/latex]<\/li>\r\n \t
  24. [latex]\\dfrac{\\sqrt{12}}{\\sqrt{3}}\\div \\sqrt{3}[\/latex]\r\n[latex]\\phantom{a}[\/latex]\r\n[latex]\\dfrac{\\sqrt{4}}{\\sqrt{1}}\\Rightarrow \\dfrac{2}{1}\\Rightarrow 2[\/latex]<\/li>\r\n \t
  25. [latex]\\dfrac{\\sqrt{10}}{\\sqrt{6}}\\div \\sqrt{2} [\/latex]\r\n[latex]\\phantom{a}[\/latex]\r\n[latex]\\dfrac{\\sqrt{5}}{\\sqrt{3}}[\/latex]<\/li>\r\n \t
  26. Does not reduce<\/li>\r\n \t
  27. [latex]\\dfrac{5x^2}{4\\sqrt{3\\cdot x^2\\cdot x\\cdot y^2\\cdot y}}\\Rightarrow \\dfrac{5x^2}{4xy\\sqrt{3xy}}\\Rightarrow \\dfrac{5x}{4y\\sqrt{3xy}}[\/latex]<\/li>\r\n \t
  28. [latex]\\dfrac{4}{5y^2\\sqrt{3x}}[\/latex]<\/li>\r\n \t
  29. [latex]\\dfrac{\\sqrt{2p^2}}{\\sqrt{3p}}\\div \\sqrt{p}[\/latex]\r\n[latex]\\phantom{a}[\/latex]\r\n[latex]\\dfrac{\\sqrt{2p}}{\\sqrt{3}}[\/latex]<\/li>\r\n \t
  30. [latex]\\dfrac{\\sqrt{8n^2}}{\\sqrt{10n}}\\div \\sqrt{2n}[\/latex]\r\n[latex]\\phantom{a}[\/latex]\r\n[latex]\\dfrac{\\sqrt{4n}}{\\sqrt{5}}\\Rightarrow \\dfrac{2\\sqrt{n}}{\\sqrt{5}}[\/latex]<\/li>\r\n<\/ol>","rendered":"
      \n
    1. [latex]12\\sqrt{5\\cdot 16}[\/latex]
      \n[latex]12\\cdot 4 \\sqrt{5}[\/latex]
      \n[latex]48\\sqrt{5}[\/latex]<\/li>\n
    2. [latex]-5\\sqrt{10\\cdot 15}[\/latex]
      \n[latex]-5\\sqrt{150}[\/latex]
      \n[latex]-5\\sqrt{25\\cdot 6}\\Rightarrow -25\\sqrt{6}[\/latex]<\/li>\n
    3. [latex]\\sqrt{15\\cdot 12\\cdot m^2}[\/latex]
      \n[latex]\\sqrt{3\\cdot 5\\cdot 3\\cdot 4\\cdot m^2}[\/latex]
      \n[latex]3\\cdot 2m\\sqrt{5}[\/latex]
      \n[latex]6m\\sqrt{5}[\/latex]<\/li>\n
    4. [latex]-5\\sqrt{5r^3\\cdot 10r^2}[\/latex]
      \n[latex]-5\\sqrt{25\\cdot 2\\cdot r^4\\cdot r}[\/latex]
      \n[latex]-25r^2\\sqrt{2r}[\/latex]<\/li>\n
    5. [latex]\\sqrt[3]{8x^7}[\/latex]
      \n[latex]\\sqrt[3]{8\\cdot x^6\\cdot x}[\/latex]
      \n[latex]2x^2 \\sqrt[3]{x}[\/latex]<\/li>\n
    6. [latex]3 \\sqrt[3]{40a^7}[\/latex]
      \n[latex]3 \\sqrt[3]{5\\cdot 8\\cdot a^6\\cdot a}[\/latex]
      \n[latex]3\\cdot 2a^2 \\sqrt[3]{5a}\\Rightarrow 6a^2 \\sqrt[3]{5a}[\/latex]<\/li>\n
    7. [latex]\\sqrt{12}+2\\sqrt{6}[\/latex]
      \n[latex]\\sqrt{4\\cdot 3}+2\\sqrt{6}[\/latex]
      \n[latex]2\\sqrt{3}+2\\sqrt{6}[\/latex]<\/li>\n
    8. [latex]\\sqrt{50}+\\sqrt{20}[\/latex]
      \n[latex]\\sqrt{25\\cdot 2}+\\sqrt{4\\cdot 5}[\/latex]
      \n[latex]5\\sqrt{2}+2\\sqrt{5}[\/latex]<\/li>\n
    9. [latex]-15\\sqrt{45}-10\\sqrt{15}[\/latex]
      \n[latex]-15\\sqrt{9\\cdot 5}-10\\sqrt{15}[\/latex]
      \n[latex]-15\\cdot 3\\sqrt{5}-10\\sqrt{15}[\/latex]
      \n[latex]-45\\sqrt{5}-10\\sqrt{15}[\/latex]<\/li>\n
    10. [latex]15\\sqrt{45}+10\\sqrt{15}[\/latex]
      \n[latex]15\\sqrt{9\\cdot 5}+10\\sqrt{15}[\/latex]
      \n[latex]15\\cdot 3\\sqrt{5}+10\\sqrt{15}[\/latex]
      \n[latex]45\\sqrt{5}+10\\sqrt{15}[\/latex]<\/li>\n
    11. [latex]25n\\sqrt{10}+5\\sqrt{20}[\/latex]
      \n[latex]25n\\sqrt{10}+5\\sqrt{4\\cdot 5}[\/latex]
      \n[latex]25n\\sqrt{10}+10\\sqrt{5}[\/latex]<\/li>\n
    12. [latex]\\sqrt{75}-3\\sqrt{45v}[\/latex]
      \n[latex]\\sqrt{25\\cdot 3}-3\\sqrt{9\\cdot 5v}[\/latex]
      \n[latex]5\\sqrt{3}-9\\sqrt{5v}[\/latex]<\/li>\n
    13. [latex]-6+2\\sqrt{2}-6\\sqrt{2}+2(\\sqrt{2})(\\sqrt{2})[\/latex]
      \n[latex]-6+2\\sqrt{2}-6\\sqrt{2}+2(2)[\/latex]
      \n[latex]-6+4+2\\sqrt{2}-6\\sqrt{2}[\/latex]
      \n[latex]-2-4\\sqrt{2}[\/latex]<\/li>\n
    14. [latex]10-4\\sqrt{3}-5\\sqrt{3}+2(\\sqrt{3})(\\sqrt{3})[\/latex]
      \n[latex]10-4\\sqrt{3}-5\\sqrt{3}+2(3)[\/latex]
      \n[latex]10+6-4\\sqrt{3}-5\\sqrt{3}[\/latex]
      \n[latex]16-9\\sqrt{3}[\/latex]<\/li>\n
    15. [latex](2\\sqrt{5})(\\sqrt{5})-\\sqrt{5}-10\\sqrt{5}+5[\/latex]
      \n[latex]2(5)-\\sqrt{5}-10\\sqrt{5}+5[\/latex]
      \n[latex]10+5-\\sqrt{5}-10\\sqrt{5}[\/latex]
      \n[latex]15-11\\sqrt{5}[\/latex]<\/li>\n
    16. [latex]10(3)+4\\sqrt{12}+5\\sqrt{15}+2\\sqrt{20}[\/latex]
      \n[latex]30+4\\sqrt{4\\cdot 3}+5\\sqrt{15}+2\\sqrt{5\\cdot 4}[\/latex]
      \n[latex]30+5\\sqrt{15}+8\\sqrt{3}+4\\sqrt{5}[\/latex]<\/li>\n
    17. [latex]3(2a)+6\\sqrt{6a^2}+\\sqrt{10a^2}+2\\sqrt{15a^2}[\/latex]
      \n[latex]6a+6a\\sqrt{6}+a\\sqrt{10}+2a\\sqrt{15}[\/latex]<\/li>\n
    18. [latex](-2\\sqrt{2p}+5\\sqrt{5})(2\\sqrt{5p})[\/latex]
      \n[latex]-4\\sqrt{10p^2}+10\\sqrt{25p}[\/latex]
      \n[latex]-4p\\sqrt{10}+50\\sqrt{p}[\/latex]<\/li>\n
    19. [latex]15+12\\sqrt{3}+20\\sqrt{3}+16(3)[\/latex]
      \n[latex]63+32\\sqrt{3}[\/latex]<\/li>\n
    20. [latex]-5\\sqrt{4m}+\\sqrt{2m}+25\\sqrt{2}-5[\/latex]
      \n[latex]-10\\sqrt{m}+\\sqrt{2m}+25\\sqrt{2}-5[\/latex]<\/li>\n
    21. [latex]\\dfrac{\\sqrt{12}}{5\\sqrt{100}}\\div \\sqrt{4}[\/latex]
      \n[latex]\\phantom{a}[\/latex]
      \n[latex]\\dfrac{\\sqrt{3}}{5\\sqrt{25}}\\Rightarrow \\dfrac{\\sqrt{3}}{5\\cdot 5}\\Rightarrow \\dfrac{\\sqrt{3}}{25}[\/latex]<\/li>\n
    22. [latex]\\dfrac{\\sqrt{15}}{2\\cdot 2}\\Rightarrow \\dfrac{\\sqrt{15}}{4}[\/latex]<\/li>\n
    23. [latex]\\dfrac{\\sqrt{5}}{4\\sqrt{125}}\\div \\sqrt{5}[\/latex]
      \n[latex]\\phantom{a}[\/latex]
      \n[latex]\\dfrac{\\sqrt{1}}{4\\sqrt{25}}\\Rightarrow \\dfrac{1}{4\\cdot 5}\\Rightarrow \\dfrac{1}{20}[\/latex]<\/li>\n
    24. [latex]\\dfrac{\\sqrt{12}}{\\sqrt{3}}\\div \\sqrt{3}[\/latex]
      \n[latex]\\phantom{a}[\/latex]
      \n[latex]\\dfrac{\\sqrt{4}}{\\sqrt{1}}\\Rightarrow \\dfrac{2}{1}\\Rightarrow 2[\/latex]<\/li>\n
    25. [latex]\\dfrac{\\sqrt{10}}{\\sqrt{6}}\\div \\sqrt{2}[\/latex]
      \n[latex]\\phantom{a}[\/latex]
      \n[latex]\\dfrac{\\sqrt{5}}{\\sqrt{3}}[\/latex]<\/li>\n
    26. Does not reduce<\/li>\n
    27. [latex]\\dfrac{5x^2}{4\\sqrt{3\\cdot x^2\\cdot x\\cdot y^2\\cdot y}}\\Rightarrow \\dfrac{5x^2}{4xy\\sqrt{3xy}}\\Rightarrow \\dfrac{5x}{4y\\sqrt{3xy}}[\/latex]<\/li>\n
    28. [latex]\\dfrac{4}{5y^2\\sqrt{3x}}[\/latex]<\/li>\n
    29. [latex]\\dfrac{\\sqrt{2p^2}}{\\sqrt{3p}}\\div \\sqrt{p}[\/latex]
      \n[latex]\\phantom{a}[\/latex]
      \n[latex]\\dfrac{\\sqrt{2p}}{\\sqrt{3}}[\/latex]<\/li>\n
    30. [latex]\\dfrac{\\sqrt{8n^2}}{\\sqrt{10n}}\\div \\sqrt{2n}[\/latex]
      \n[latex]\\phantom{a}[\/latex]
      \n[latex]\\dfrac{\\sqrt{4n}}{\\sqrt{5}}\\Rightarrow \\dfrac{2\\sqrt{n}}{\\sqrt{5}}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":85,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"back-matter-type":[],"contributor":[],"license":[56],"class_list":["post-1960","back-matter","type-back-matter","status-publish","hentry","license-cc-by-nc-sa"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1960","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":3,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1960\/revisions"}],"predecessor-version":[{"id":2232,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1960\/revisions\/2232"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1960\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1960"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1960"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1960"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1960"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}