{"id":1962,"date":"2021-12-02T19:40:12","date_gmt":"2021-12-03T00:40:12","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-9-5\/"},"modified":"2022-11-02T10:38:45","modified_gmt":"2022-11-02T14:38:45","slug":"answer-key-9-5","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-9-5\/","title":{"raw":"Answer Key 9.5","rendered":"Answer Key 9.5"},"content":{"raw":"
    \n \t
  1. [latex]\\dfrac{4+2\\sqrt{3}}{\\sqrt{3}}\\cdot \\dfrac{\\sqrt{3}}{\\sqrt{3}}\\Rightarrow \\dfrac{4\\sqrt{3}+2(3)}{3}\\Rightarrow \\dfrac{4\\sqrt{3}+6}{3}[\/latex]<\/li>\n \t
  2. [latex]\\dfrac{-4+\\sqrt{3}}{4\\sqrt{3}}\\cdot \\dfrac{\\sqrt{3}}{\\sqrt{3}}\\Rightarrow \\dfrac{-4\\sqrt{3}+3}{4(3)}\\Rightarrow \\dfrac{-4\\sqrt{3}+3}{12}[\/latex]<\/li>\n \t
  3. [latex]\\dfrac{4+2\\sqrt{3}}{5\\sqrt{6}}\\cdot \\dfrac{\\sqrt{6}}{\\sqrt{6}}\\Rightarrow \\dfrac{4\\sqrt{6}+2\\sqrt{18}}{5(6)}\\Rightarrow \\dfrac{4\\sqrt{6}+6\\sqrt{2}}{30}\\Rightarrow \\dfrac{2\\sqrt{6}+3\\sqrt{2}}{15}[\/latex]<\/li>\n \t
  4. [latex]\\dfrac{2\\sqrt{3}-2}{2\\sqrt{3}}\\cdot \\dfrac{\\sqrt{3}}{\\sqrt{3}}\\Rightarrow \\dfrac{2(3)-2\\sqrt{3}}{2(3)}\\Rightarrow \\dfrac{6-2\\sqrt{3}}{6}\\Rightarrow \\dfrac{3-\\sqrt{3}}{3}[\/latex]<\/li>\n \t
  5. [latex]\\dfrac{2-5\\sqrt{5}}{4\\sqrt{3}}\\cdot \\dfrac{\\sqrt{3}}{\\sqrt{3}}\\Rightarrow \\dfrac{2\\sqrt{3}-5\\sqrt{15}}{4(3)}\\Rightarrow \\dfrac{2\\sqrt{3}-5\\sqrt{15}}{12}[\/latex]<\/li>\n \t
  6. [latex]\\dfrac{\\sqrt{5}+4}{4\\sqrt{5}}\\cdot \\dfrac{\\sqrt{5}}{\\sqrt{5}}\\Rightarrow \\dfrac{5+4\\sqrt{5}}{4(5)}\\Rightarrow \\dfrac{5+4\\sqrt{5}}{20}[\/latex]<\/li>\n \t
  7. [latex]\\dfrac{\\sqrt{2}-3\\sqrt{3}}{\\sqrt{3}}\\cdot \\dfrac{\\sqrt{3}}{\\sqrt{3}}\\Rightarrow \\dfrac{\\sqrt{6}-3(3)}{3}\\Rightarrow \\dfrac{\\sqrt{6}-9}{3}[\/latex]<\/li>\n \t
  8. [latex]\\dfrac{\\sqrt{5}-\\sqrt{2}}{3\\sqrt{6}}\\cdot \\dfrac{\\sqrt{6}}{\\sqrt{6}}\\Rightarrow \\dfrac{\\sqrt{30}-\\sqrt{12}}{3(6)}\\Rightarrow \\dfrac{\\sqrt{30}-2\\sqrt{3}}{18}[\/latex]<\/li>\n \t
  9. [latex]\\dfrac{5}{3\\sqrt{5}+\\sqrt{2}}\\cdot \\dfrac{3\\sqrt{5}-\\sqrt{2}}{3\\sqrt{5}-\\sqrt{2}}\\Rightarrow \\dfrac{15\\sqrt{5}-5\\sqrt{2}}{9(5)-2}\\Rightarrow \\dfrac{15\\sqrt{5}-5\\sqrt{2}}{43}[\/latex]<\/li>\n \t
  10. [latex]\\dfrac{5}{\\sqrt{3}+4\\sqrt{5}}\\cdot \\dfrac{\\sqrt{3}-4\\sqrt{5}}{\\sqrt{3}-4\\sqrt{5}}\\Rightarrow \\dfrac{5\\sqrt{3}-20\\sqrt{5}}{3-16(5)}\\Rightarrow \\dfrac{5\\sqrt{3}-20\\sqrt{5}}{-77}\\Rightarrow \\dfrac{20\\sqrt{5}-5\\sqrt{3}}{77}[\/latex]<\/li>\n \t
  11. [latex]\\dfrac{2}{5+\\sqrt{2}}\\cdot \\dfrac{5-\\sqrt{2}}{5-\\sqrt{2}}\\Rightarrow \\dfrac{10-2\\sqrt{2}}{25-2}\\Rightarrow \\dfrac{10-2\\sqrt{2}}{23}[\/latex]<\/li>\n \t
  12. [latex]\\dfrac{5}{2\\sqrt{3}-\\sqrt{2}}\\cdot \\dfrac{2\\sqrt{3}+\\sqrt{2}}{2\\sqrt{3}+\\sqrt{2}}\\Rightarrow \\dfrac{10\\sqrt{3}+5\\sqrt{2}}{4(3)-2}\\Rightarrow \\dfrac{10\\sqrt{3}+5\\sqrt{2}}{10}\\Rightarrow \\dfrac{2\\sqrt{3}+\\sqrt{2}}{2}[\/latex]<\/li>\n \t
  13. [latex]\\dfrac{3}{4-\\sqrt{3}}\\cdot \\dfrac{4+\\sqrt{3}}{4+\\sqrt{3}}\\Rightarrow \\dfrac{12+3\\sqrt{3}}{16-3}\\Rightarrow \\dfrac{12+3\\sqrt{3}}{13}[\/latex]<\/li>\n \t
  14. [latex]\\dfrac{4}{\\sqrt{2}-2}\\cdot \\dfrac{\\sqrt{2}+2}{\\sqrt{2}+2}\\Rightarrow \\dfrac{4\\sqrt{2}+8}{2-4}\\Rightarrow \\dfrac{4\\sqrt{2}+8}{-2}\\Rightarrow -2\\sqrt{2}-4[\/latex]<\/li>\n \t
  15. [latex]\\dfrac{4}{3+\\sqrt{5}}\\cdot \\dfrac{3-\\sqrt{5}}{3-\\sqrt{5}}\\Rightarrow \\dfrac{12-4\\sqrt{5}}{9-5}\\Rightarrow \\dfrac{12-4\\sqrt{5}}{4}\\Rightarrow 3-\\sqrt{5}[\/latex]<\/li>\n \t
  16. [latex]\\dfrac{2}{\\sqrt{5}+2\\sqrt{3}}\\cdot \\dfrac{\\sqrt{5}-2\\sqrt{3}}{\\sqrt{5}-2\\sqrt{3}}\\Rightarrow \\dfrac{2\\sqrt{5}-4\\sqrt{3}}{5-4(3)}\\Rightarrow \\dfrac{2\\sqrt{5}-4\\sqrt{3}}{-7}[\/latex]<\/li>\n \t
  17. [latex]\\dfrac{-3+2\\sqrt{3}}{\\sqrt{3}+2}\\cdot \\dfrac{\\sqrt{3}-2}{\\sqrt{3}-2}\\Rightarrow \\dfrac{-3\\sqrt{3}+6+2(3)-4\\sqrt{3}}{3-4}\\Rightarrow \\dfrac{12-7\\sqrt{3}}{-1}\\Rightarrow[\/latex]\n[latex]\\phantom{a}[\/latex]\n[latex]-12+7\\sqrt{3}[\/latex]<\/li>\n \t
  18. [latex]\\dfrac{4+\\sqrt{5}}{2+2\\sqrt{5}}\\cdot \\dfrac{2-2\\sqrt{5}}{2-2\\sqrt{5}}\\Rightarrow \\dfrac{8-8\\sqrt{5}+2\\sqrt{5}-2(5)}{4-4(5)}\\Rightarrow \\dfrac{-2-6\\sqrt{5}}{-16}\\Rightarrow \\dfrac{1+3\\sqrt{5}}{8}[\/latex]<\/li>\n \t
  19. [latex]\\dfrac{2-\\sqrt{3}}{1+\\sqrt{2}}\\cdot \\dfrac{1-\\sqrt{2}}{1-\\sqrt{2}}\\Rightarrow \\dfrac{2-2\\sqrt{2}-\\sqrt{3}+\\sqrt{6}}{1-2}\\Rightarrow \\dfrac{2-2\\sqrt{2}-\\sqrt{3}+\\sqrt{6}}{-1}[\/latex]\n[latex]\\phantom{a}[\/latex]\n[latex]\\Rightarrow2\\sqrt{2}+\\sqrt{3}-\\sqrt{6}-2[\/latex]<\/li>\n \t
  20. [latex]\\dfrac{-1+\\sqrt{3}}{\\sqrt{3}-1}\\cdot \\dfrac{\\sqrt{3}+1}{\\sqrt{3}+1}\\Rightarrow \\dfrac{-\\sqrt{3}-1+3+\\sqrt{3}}{3-1}\\Rightarrow \\dfrac{2}{2}\\Rightarrow 1[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex]\\dfrac{4+2\\sqrt{3}}{\\sqrt{3}}\\cdot \\dfrac{\\sqrt{3}}{\\sqrt{3}}\\Rightarrow \\dfrac{4\\sqrt{3}+2(3)}{3}\\Rightarrow \\dfrac{4\\sqrt{3}+6}{3}[\/latex]<\/li>\n
    2. [latex]\\dfrac{-4+\\sqrt{3}}{4\\sqrt{3}}\\cdot \\dfrac{\\sqrt{3}}{\\sqrt{3}}\\Rightarrow \\dfrac{-4\\sqrt{3}+3}{4(3)}\\Rightarrow \\dfrac{-4\\sqrt{3}+3}{12}[\/latex]<\/li>\n
    3. [latex]\\dfrac{4+2\\sqrt{3}}{5\\sqrt{6}}\\cdot \\dfrac{\\sqrt{6}}{\\sqrt{6}}\\Rightarrow \\dfrac{4\\sqrt{6}+2\\sqrt{18}}{5(6)}\\Rightarrow \\dfrac{4\\sqrt{6}+6\\sqrt{2}}{30}\\Rightarrow \\dfrac{2\\sqrt{6}+3\\sqrt{2}}{15}[\/latex]<\/li>\n
    4. [latex]\\dfrac{2\\sqrt{3}-2}{2\\sqrt{3}}\\cdot \\dfrac{\\sqrt{3}}{\\sqrt{3}}\\Rightarrow \\dfrac{2(3)-2\\sqrt{3}}{2(3)}\\Rightarrow \\dfrac{6-2\\sqrt{3}}{6}\\Rightarrow \\dfrac{3-\\sqrt{3}}{3}[\/latex]<\/li>\n
    5. [latex]\\dfrac{2-5\\sqrt{5}}{4\\sqrt{3}}\\cdot \\dfrac{\\sqrt{3}}{\\sqrt{3}}\\Rightarrow \\dfrac{2\\sqrt{3}-5\\sqrt{15}}{4(3)}\\Rightarrow \\dfrac{2\\sqrt{3}-5\\sqrt{15}}{12}[\/latex]<\/li>\n
    6. [latex]\\dfrac{\\sqrt{5}+4}{4\\sqrt{5}}\\cdot \\dfrac{\\sqrt{5}}{\\sqrt{5}}\\Rightarrow \\dfrac{5+4\\sqrt{5}}{4(5)}\\Rightarrow \\dfrac{5+4\\sqrt{5}}{20}[\/latex]<\/li>\n
    7. [latex]\\dfrac{\\sqrt{2}-3\\sqrt{3}}{\\sqrt{3}}\\cdot \\dfrac{\\sqrt{3}}{\\sqrt{3}}\\Rightarrow \\dfrac{\\sqrt{6}-3(3)}{3}\\Rightarrow \\dfrac{\\sqrt{6}-9}{3}[\/latex]<\/li>\n
    8. [latex]\\dfrac{\\sqrt{5}-\\sqrt{2}}{3\\sqrt{6}}\\cdot \\dfrac{\\sqrt{6}}{\\sqrt{6}}\\Rightarrow \\dfrac{\\sqrt{30}-\\sqrt{12}}{3(6)}\\Rightarrow \\dfrac{\\sqrt{30}-2\\sqrt{3}}{18}[\/latex]<\/li>\n
    9. [latex]\\dfrac{5}{3\\sqrt{5}+\\sqrt{2}}\\cdot \\dfrac{3\\sqrt{5}-\\sqrt{2}}{3\\sqrt{5}-\\sqrt{2}}\\Rightarrow \\dfrac{15\\sqrt{5}-5\\sqrt{2}}{9(5)-2}\\Rightarrow \\dfrac{15\\sqrt{5}-5\\sqrt{2}}{43}[\/latex]<\/li>\n
    10. [latex]\\dfrac{5}{\\sqrt{3}+4\\sqrt{5}}\\cdot \\dfrac{\\sqrt{3}-4\\sqrt{5}}{\\sqrt{3}-4\\sqrt{5}}\\Rightarrow \\dfrac{5\\sqrt{3}-20\\sqrt{5}}{3-16(5)}\\Rightarrow \\dfrac{5\\sqrt{3}-20\\sqrt{5}}{-77}\\Rightarrow \\dfrac{20\\sqrt{5}-5\\sqrt{3}}{77}[\/latex]<\/li>\n
    11. [latex]\\dfrac{2}{5+\\sqrt{2}}\\cdot \\dfrac{5-\\sqrt{2}}{5-\\sqrt{2}}\\Rightarrow \\dfrac{10-2\\sqrt{2}}{25-2}\\Rightarrow \\dfrac{10-2\\sqrt{2}}{23}[\/latex]<\/li>\n
    12. [latex]\\dfrac{5}{2\\sqrt{3}-\\sqrt{2}}\\cdot \\dfrac{2\\sqrt{3}+\\sqrt{2}}{2\\sqrt{3}+\\sqrt{2}}\\Rightarrow \\dfrac{10\\sqrt{3}+5\\sqrt{2}}{4(3)-2}\\Rightarrow \\dfrac{10\\sqrt{3}+5\\sqrt{2}}{10}\\Rightarrow \\dfrac{2\\sqrt{3}+\\sqrt{2}}{2}[\/latex]<\/li>\n
    13. [latex]\\dfrac{3}{4-\\sqrt{3}}\\cdot \\dfrac{4+\\sqrt{3}}{4+\\sqrt{3}}\\Rightarrow \\dfrac{12+3\\sqrt{3}}{16-3}\\Rightarrow \\dfrac{12+3\\sqrt{3}}{13}[\/latex]<\/li>\n
    14. [latex]\\dfrac{4}{\\sqrt{2}-2}\\cdot \\dfrac{\\sqrt{2}+2}{\\sqrt{2}+2}\\Rightarrow \\dfrac{4\\sqrt{2}+8}{2-4}\\Rightarrow \\dfrac{4\\sqrt{2}+8}{-2}\\Rightarrow -2\\sqrt{2}-4[\/latex]<\/li>\n
    15. [latex]\\dfrac{4}{3+\\sqrt{5}}\\cdot \\dfrac{3-\\sqrt{5}}{3-\\sqrt{5}}\\Rightarrow \\dfrac{12-4\\sqrt{5}}{9-5}\\Rightarrow \\dfrac{12-4\\sqrt{5}}{4}\\Rightarrow 3-\\sqrt{5}[\/latex]<\/li>\n
    16. [latex]\\dfrac{2}{\\sqrt{5}+2\\sqrt{3}}\\cdot \\dfrac{\\sqrt{5}-2\\sqrt{3}}{\\sqrt{5}-2\\sqrt{3}}\\Rightarrow \\dfrac{2\\sqrt{5}-4\\sqrt{3}}{5-4(3)}\\Rightarrow \\dfrac{2\\sqrt{5}-4\\sqrt{3}}{-7}[\/latex]<\/li>\n
    17. [latex]\\dfrac{-3+2\\sqrt{3}}{\\sqrt{3}+2}\\cdot \\dfrac{\\sqrt{3}-2}{\\sqrt{3}-2}\\Rightarrow \\dfrac{-3\\sqrt{3}+6+2(3)-4\\sqrt{3}}{3-4}\\Rightarrow \\dfrac{12-7\\sqrt{3}}{-1}\\Rightarrow[\/latex]
      \n[latex]\\phantom{a}[\/latex]
      \n[latex]-12+7\\sqrt{3}[\/latex]<\/li>\n
    18. [latex]\\dfrac{4+\\sqrt{5}}{2+2\\sqrt{5}}\\cdot \\dfrac{2-2\\sqrt{5}}{2-2\\sqrt{5}}\\Rightarrow \\dfrac{8-8\\sqrt{5}+2\\sqrt{5}-2(5)}{4-4(5)}\\Rightarrow \\dfrac{-2-6\\sqrt{5}}{-16}\\Rightarrow \\dfrac{1+3\\sqrt{5}}{8}[\/latex]<\/li>\n
    19. [latex]\\dfrac{2-\\sqrt{3}}{1+\\sqrt{2}}\\cdot \\dfrac{1-\\sqrt{2}}{1-\\sqrt{2}}\\Rightarrow \\dfrac{2-2\\sqrt{2}-\\sqrt{3}+\\sqrt{6}}{1-2}\\Rightarrow \\dfrac{2-2\\sqrt{2}-\\sqrt{3}+\\sqrt{6}}{-1}[\/latex]
      \n[latex]\\phantom{a}[\/latex]
      \n[latex]\\Rightarrow2\\sqrt{2}+\\sqrt{3}-\\sqrt{6}-2[\/latex]<\/li>\n
    20. [latex]\\dfrac{-1+\\sqrt{3}}{\\sqrt{3}-1}\\cdot \\dfrac{\\sqrt{3}+1}{\\sqrt{3}+1}\\Rightarrow \\dfrac{-\\sqrt{3}-1+3+\\sqrt{3}}{3-1}\\Rightarrow \\dfrac{2}{2}\\Rightarrow 1[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":86,"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-1962","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\/1962","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":1,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1962\/revisions"}],"predecessor-version":[{"id":1963,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1962\/revisions\/1963"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1962\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1962"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1962"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1962"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1962"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}