{"id":1704,"date":"2019-08-06T16:43:58","date_gmt":"2019-08-06T20:43:58","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1704"},"modified":"2019-08-06T16:50:24","modified_gmt":"2019-08-06T20:50:24","slug":"answer-key-9-5","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-9-5\/","title":{"raw":"Answer Key 9.5","rendered":"Answer Key 9.5"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\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}\\)<\/li>\r\n \t
  2. \\(\\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}\\)<\/li>\r\n \t
  3. \\(\\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}\\)<\/li>\r\n \t
  4. \\(\\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}\\)<\/li>\r\n \t
  5. \\(\\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}\\)<\/li>\r\n \t
  6. \\(\\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}\\)<\/li>\r\n \t
  7. \\(\\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}\\)<\/li>\r\n \t
  8. \\(\\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}\\)<\/li>\r\n \t
  9. \\(\\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}\\)<\/li>\r\n \t
  10. \\(\\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}\\)<\/li>\r\n \t
  11. \\(\\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}\\)<\/li>\r\n \t
  12. \\(\\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}\\)<\/li>\r\n \t
  13. \\(\\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}\\)<\/li>\r\n \t
  14. \\(\\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\\)<\/li>\r\n \t
  15. \\(\\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}\\)<\/li>\r\n \t
  16. \\(\\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}\\)<\/li>\r\n \t
  17. \\(\\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 \\\\ \\)\r\n\\(-12+7\\sqrt{3}\\)<\/li>\r\n \t
  18. \\(\\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}\\)<\/li>\r\n \t
  19. \\(\\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}\\Rightarrow \\\\ \\)\r\n\\(2\\sqrt{2}+\\sqrt{3}-\\sqrt{6}-2\\)<\/li>\r\n \t
  20. \\(\\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\\)<\/li>\r\n<\/ol>","rendered":"
      \n
    1. \"\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}\"<\/li>\n
    2. \"\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}\"<\/li>\n
    3. \"\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}\"<\/li>\n
    4. \"\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}\"<\/li>\n
    5. \"\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}\"<\/li>\n
    6. \"\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}\"<\/li>\n
    7. \"\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}\"<\/li>\n
    8. \"\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}\"<\/li>\n
    9. \"\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}\"<\/li>\n
    10. \"\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}\"<\/li>\n
    11. \"\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}\"<\/li>\n
    12. \"\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}\"<\/li>\n
    13. \"\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}\"<\/li>\n
    14. \"\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\"<\/li>\n
    15. \"\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}\"<\/li>\n
    16. \"\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}\"<\/li>\n
    17. \"\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 \\\"
      \n\"-12+7\sqrt{3}\"<\/li>\n
    18. \"\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}\"<\/li>\n
    19. \"\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}\Rightarrow \\\"
      \n\"2\sqrt{2}+\sqrt{3}-\sqrt{6}-2\"<\/li>\n
    20. \"\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\"<\/li>\n<\/ol>\n","protected":false},"author":727,"menu_order":81,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-1704","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1704","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/users\/727"}],"version-history":[{"count":3,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1704\/revisions"}],"predecessor-version":[{"id":1707,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1704\/revisions\/1707"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1704\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=1704"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=1704"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=1704"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=1704"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}