{"id":1696,"date":"2019-08-06T14:22:58","date_gmt":"2019-08-06T18:22:58","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1696"},"modified":"2019-11-04T13:59:54","modified_gmt":"2019-11-04T18:59:54","slug":"answer-key-9-4","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-9-4\/","title":{"raw":"Answer Key 9.4","rendered":"Answer Key 9.4"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(12\\sqrt{5\\cdot 16}\\)\r\n\\(12\\cdot 4 \\sqrt{5}\\)\r\n\\(48\\sqrt{5}\\)<\/li>\r\n \t
  2. \\(-5\\sqrt{10\\cdot 15}\\)\r\n\\(-5\\sqrt{150}\\)\r\n\\(-5\\sqrt{25\\cdot 6}\\Rightarrow -25\\sqrt{6}\\)<\/li>\r\n \t
  3. \\(\\sqrt{15\\cdot 12\\cdot m^2}\\)\r\n\\(\\sqrt{3\\cdot 5\\cdot 3\\cdot 4\\cdot m^2}\\)\r\n\\(3\\cdot 2m\\sqrt{5}\\)\r\n\\(6m\\sqrt{5}\\)<\/li>\r\n \t
  4. \\(-5\\sqrt{5r^3\\cdot 10r^2}\\)\r\n\\(-5\\sqrt{25\\cdot 2\\cdot r^4\\cdot r}\\)\r\n\\(-25r^2\\sqrt{2r}\\)<\/li>\r\n \t
  5. \\(\\sqrt[3]{8x^7}\\)\r\n\\(\\sqrt[3]{8\\cdot x^6\\cdot x}\\)\r\n\\(2x^2 \\sqrt[3]{x}\\)<\/li>\r\n \t
  6. \\(3 \\sqrt[3]{40a^7}\\)\r\n\\(3 \\sqrt[3]{5\\cdot 8\\cdot a^6\\cdot a}\\)\r\n\\(3\\cdot 2a^2 \\sqrt[3]{5a}\\Rightarrow 6a^2 \\sqrt[3]{5a}\\)<\/li>\r\n \t
  7. \\(\\sqrt{12}+2\\sqrt{6}\\)\r\n\\(\\sqrt{4\\cdot 3}+2\\sqrt{6}\\)\r\n\\(2\\sqrt{3}+2\\sqrt{6}\\)<\/li>\r\n \t
  8. \\(\\sqrt{50}+\\sqrt{20}\\)\r\n\\(\\sqrt{25\\cdot 2}+\\sqrt{4\\cdot 5}\\)\r\n\\(5\\sqrt{2}+2\\sqrt{5}\\)<\/li>\r\n \t
  9. \\(-15\\sqrt{45}-10\\sqrt{15}\\)\r\n\\(-15\\sqrt{9\\cdot 5}-10\\sqrt{15}\\)\r\n\\(-15\\cdot 3\\sqrt{5}-10\\sqrt{15}\\)\r\n\\(-45\\sqrt{5}-10\\sqrt{15}\\)<\/li>\r\n \t
  10. \\(15\\sqrt{45}+10\\sqrt{15}\\)\r\n\\(15\\sqrt{9\\cdot 5}+10\\sqrt{15}\\)\r\n\\(15\\cdot 3\\sqrt{5}+10\\sqrt{15}\\)\r\n\\(45\\sqrt{5}+10\\sqrt{15}\\)<\/li>\r\n \t
  11. \\(25n\\sqrt{10}+5\\sqrt{20}\\)\r\n\\(25n\\sqrt{10}+5\\sqrt{4\\cdot 5}\\)\r\n\\(25n\\sqrt{10}+10\\sqrt{5}\\)<\/li>\r\n \t
  12. \\(\\sqrt{75}-3\\sqrt{45v}\\)\r\n\\(\\sqrt{25\\cdot 3}-3\\sqrt{9\\cdot 5v}\\)\r\n\\(5\\sqrt{3}-9\\sqrt{5v}\\)<\/li>\r\n \t
  13. \\(-6+2\\sqrt{2}-6\\sqrt{2}+2(\\sqrt{2})(\\sqrt{2})\\)\r\n\\(-6+2\\sqrt{2}-6\\sqrt{2}+2(2)\\)\r\n\\(-6+4+2\\sqrt{2}-6\\sqrt{2}\\)\r\n\\(-2-4\\sqrt{2}\\)<\/li>\r\n \t
  14. \\(10-4\\sqrt{3}-5\\sqrt{3}+2(\\sqrt{3})(\\sqrt{3})\\)\r\n\\(10-4\\sqrt{3}-5\\sqrt{3}+2(3)\\)\r\n\\(10+6-4\\sqrt{3}-5\\sqrt{3}\\)\r\n\\(16-9\\sqrt{3}\\)<\/li>\r\n \t
  15. \\((2\\sqrt{5})(\\sqrt{5})-\\sqrt{5}-10\\sqrt{5}+5\\)\r\n\\(2(5)-\\sqrt{5}-10\\sqrt{5}+5\\)\r\n\\(10+5-\\sqrt{5}-10\\sqrt{5}\\)\r\n\\(15-11\\sqrt{5}\\)<\/li>\r\n \t
  16. \\(10(3)+4\\sqrt{12}+5\\sqrt{15}+2\\sqrt{20}\\)\r\n\\(30+4\\sqrt{4\\cdot 3}+5\\sqrt{15}+2\\sqrt{5\\cdot 4}\\)\r\n\\(30+5\\sqrt{15}+8\\sqrt{3}+4\\sqrt{5}\\)<\/li>\r\n \t
  17. \\(3(2a)+6\\sqrt{6a^2}+\\sqrt{10a^2}+2\\sqrt{15a^2}\\)\r\n\\(6a+6a\\sqrt{6}+a\\sqrt{10}+2a\\sqrt{15}\\)<\/li>\r\n \t
  18. \\((-2\\sqrt{2p}+5\\sqrt{5})(2\\sqrt{5p})\\)\r\n\\(-4\\sqrt{10p^2}+10\\sqrt{25p}\\)\r\n\\(-4p\\sqrt{10}+50\\sqrt{p}\\)<\/li>\r\n \t
  19. \\(15+12\\sqrt{3}+20\\sqrt{3}+16(3)\\)\r\n\\(63+32\\sqrt{3}\\)<\/li>\r\n \t
  20. \\(-5\\sqrt{4m}+\\sqrt{2m}+25\\sqrt{2}-5\\)\r\n\\(-10\\sqrt{m}+\\sqrt{2m}+25\\sqrt{2}-5\\)<\/li>\r\n \t
  21. \\(\\phantom{1}\\)\r\n\\(\\dfrac{\\sqrt{12}}{5\\sqrt{100}}\\div \\sqrt{4} \\\\ \\)\r\n\\(\\dfrac{\\sqrt{3}}{5\\sqrt{25}}\\Rightarrow \\dfrac{\\sqrt{3}}{5\\cdot 5}\\Rightarrow \\dfrac{\\sqrt{3}}{25}\\)<\/li>\r\n \t
  22. \\(\\dfrac{\\sqrt{15}}{2\\cdot 2}\\Rightarrow \\dfrac{\\sqrt{15}}{4}\\)<\/li>\r\n \t
  23. \\(\\phantom{1}\\)\r\n\\(\\dfrac{\\sqrt{5}}{4\\sqrt{125}}\\div \\sqrt{5} \\\\ \\)\r\n\\(\\dfrac{\\sqrt{1}}{4\\sqrt{25}}\\Rightarrow \\dfrac{1}{4\\cdot 5}\\Rightarrow \\dfrac{1}{20}\\)<\/li>\r\n \t
  24. \\(\\phantom{1}\\)\r\n\\(\\dfrac{\\sqrt{12}}{\\sqrt{3}}\\div \\sqrt{3} \\\\ \\)\r\n\\(\\dfrac{\\sqrt{4}}{\\sqrt{1}}\\Rightarrow \\dfrac{2}{1}\\Rightarrow 2\\)<\/li>\r\n \t
  25. \\(\\phantom{1}\\)\r\n\\(\\dfrac{\\sqrt{10}}{\\sqrt{6}}\\div \\sqrt{2} \\\\ \\)\r\n\\(\\dfrac{\\sqrt{5}}{\\sqrt{3}}\\)<\/li>\r\n \t
  26. Does not reduce<\/li>\r\n \t
  27. \\(\\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}}\\)<\/li>\r\n \t
  28. \\(\\dfrac{4}{5y^2\\sqrt{3x}}\\)<\/li>\r\n \t
  29. \\(\\phantom{1}\\)\r\n\\(\\dfrac{\\sqrt{2p^2}}{\\sqrt{3p}}\\div \\sqrt{p} \\\\ \\)\r\n\\(\\dfrac{\\sqrt{2p}}{\\sqrt{3}}\\)<\/li>\r\n \t
  30. \\(\\phantom{1}\\)\r\n\\(\\dfrac{\\sqrt{8n^2}}{\\sqrt{10n}}\\div \\sqrt{2n} \\\\ \\)\r\n\\(\\dfrac{\\sqrt{4n}}{\\sqrt{5}}\\Rightarrow \\dfrac{2\\sqrt{n}}{\\sqrt{5}}\\)<\/li>\r\n<\/ol>","rendered":"
      \n
    1. \"12\sqrt{5\cdot 16}\"
      \n\"12\cdot 4 \sqrt{5}\"
      \n\"48\sqrt{5}\"<\/li>\n
    2. \"-5\sqrt{10\cdot 15}\"
      \n\"-5\sqrt{150}\"
      \n\"-5\sqrt{25\cdot 6}\Rightarrow -25\sqrt{6}\"<\/li>\n
    3. \"\sqrt{15\cdot 12\cdot m^2}\"
      \n\"\sqrt{3\cdot 5\cdot 3\cdot 4\cdot m^2}\"
      \n\"3\cdot 2m\sqrt{5}\"
      \n\"6m\sqrt{5}\"<\/li>\n
    4. \"-5\sqrt{5r^3\cdot 10r^2}\"
      \n\"-5\sqrt{25\cdot 2\cdot r^4\cdot r}\"
      \n\"-25r^2\sqrt{2r}\"<\/li>\n
    5. \"\sqrt[3]{8x^7}\"
      \n\"\sqrt[3]{8\cdot x^6\cdot x}\"
      \n\"2x^2 \sqrt[3]{x}\"<\/li>\n
    6. \"3 \sqrt[3]{40a^7}\"
      \n\"3 \sqrt[3]{5\cdot 8\cdot a^6\cdot a}\"
      \n\"3\cdot 2a^2 \sqrt[3]{5a}\Rightarrow 6a^2 \sqrt[3]{5a}\"<\/li>\n
    7. \"\sqrt{12}+2\sqrt{6}\"
      \n\"\sqrt{4\cdot 3}+2\sqrt{6}\"
      \n\"2\sqrt{3}+2\sqrt{6}\"<\/li>\n
    8. \"\sqrt{50}+\sqrt{20}\"
      \n\"\sqrt{25\cdot 2}+\sqrt{4\cdot 5}\"
      \n\"5\sqrt{2}+2\sqrt{5}\"<\/li>\n
    9. \"-15\sqrt{45}-10\sqrt{15}\"
      \n\"-15\sqrt{9\cdot 5}-10\sqrt{15}\"
      \n\"-15\cdot 3\sqrt{5}-10\sqrt{15}\"
      \n\"-45\sqrt{5}-10\sqrt{15}\"<\/li>\n
    10. \"15\sqrt{45}+10\sqrt{15}\"
      \n\"15\sqrt{9\cdot 5}+10\sqrt{15}\"
      \n\"15\cdot 3\sqrt{5}+10\sqrt{15}\"
      \n\"45\sqrt{5}+10\sqrt{15}\"<\/li>\n
    11. \"25n\sqrt{10}+5\sqrt{20}\"
      \n\"25n\sqrt{10}+5\sqrt{4\cdot 5}\"
      \n\"25n\sqrt{10}+10\sqrt{5}\"<\/li>\n
    12. \"\sqrt{75}-3\sqrt{45v}\"
      \n\"\sqrt{25\cdot 3}-3\sqrt{9\cdot 5v}\"
      \n\"5\sqrt{3}-9\sqrt{5v}\"<\/li>\n
    13. \"-6+2\sqrt{2}-6\sqrt{2}+2(\sqrt{2})(\sqrt{2})\"
      \n\"-6+2\sqrt{2}-6\sqrt{2}+2(2)\"
      \n\"-6+4+2\sqrt{2}-6\sqrt{2}\"
      \n\"-2-4\sqrt{2}\"<\/li>\n
    14. \"10-4\sqrt{3}-5\sqrt{3}+2(\sqrt{3})(\sqrt{3})\"
      \n\"10-4\sqrt{3}-5\sqrt{3}+2(3)\"
      \n\"10+6-4\sqrt{3}-5\sqrt{3}\"
      \n\"16-9\sqrt{3}\"<\/li>\n
    15. \"(2\sqrt{5})(\sqrt{5})-\sqrt{5}-10\sqrt{5}+5\"
      \n\"2(5)-\sqrt{5}-10\sqrt{5}+5\"
      \n\"10+5-\sqrt{5}-10\sqrt{5}\"
      \n\"15-11\sqrt{5}\"<\/li>\n
    16. \"10(3)+4\sqrt{12}+5\sqrt{15}+2\sqrt{20}\"
      \n\"30+4\sqrt{4\cdot 3}+5\sqrt{15}+2\sqrt{5\cdot 4}\"
      \n\"30+5\sqrt{15}+8\sqrt{3}+4\sqrt{5}\"<\/li>\n
    17. \"3(2a)+6\sqrt{6a^2}+\sqrt{10a^2}+2\sqrt{15a^2}\"
      \n\"6a+6a\sqrt{6}+a\sqrt{10}+2a\sqrt{15}\"<\/li>\n
    18. \"(-2\sqrt{2p}+5\sqrt{5})(2\sqrt{5p})\"
      \n\"-4\sqrt{10p^2}+10\sqrt{25p}\"
      \n\"-4p\sqrt{10}+50\sqrt{p}\"<\/li>\n
    19. \"15+12\sqrt{3}+20\sqrt{3}+16(3)\"
      \n\"63+32\sqrt{3}\"<\/li>\n
    20. \"-5\sqrt{4m}+\sqrt{2m}+25\sqrt{2}-5\"
      \n\"-10\sqrt{m}+\sqrt{2m}+25\sqrt{2}-5\"<\/li>\n
    21. \"\phantom{1}\"
      \n\"\dfrac{\sqrt{12}}{5\sqrt{100}}\div \sqrt{4} \\\"
      \n\"\dfrac{\sqrt{3}}{5\sqrt{25}}\Rightarrow \dfrac{\sqrt{3}}{5\cdot 5}\Rightarrow \dfrac{\sqrt{3}}{25}\"<\/li>\n
    22. \"\dfrac{\sqrt{15}}{2\cdot 2}\Rightarrow \dfrac{\sqrt{15}}{4}\"<\/li>\n
    23. \"\phantom{1}\"
      \n\"\dfrac{\sqrt{5}}{4\sqrt{125}}\div \sqrt{5} \\\"
      \n\"\dfrac{\sqrt{1}}{4\sqrt{25}}\Rightarrow \dfrac{1}{4\cdot 5}\Rightarrow \dfrac{1}{20}\"<\/li>\n
    24. \"\phantom{1}\"
      \n\"\dfrac{\sqrt{12}}{\sqrt{3}}\div \sqrt{3} \\\"
      \n\"\dfrac{\sqrt{4}}{\sqrt{1}}\Rightarrow \dfrac{2}{1}\Rightarrow 2\"<\/li>\n
    25. \"\phantom{1}\"
      \n\"\dfrac{\sqrt{10}}{\sqrt{6}}\div \sqrt{2} \\\"
      \n\"\dfrac{\sqrt{5}}{\sqrt{3}}\"<\/li>\n
    26. Does not reduce<\/li>\n
    27. \"\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}}\"<\/li>\n
    28. \"\dfrac{4}{5y^2\sqrt{3x}}\"<\/li>\n
    29. \"\phantom{1}\"
      \n\"\dfrac{\sqrt{2p^2}}{\sqrt{3p}}\div \sqrt{p} \\\"
      \n\"\dfrac{\sqrt{2p}}{\sqrt{3}}\"<\/li>\n
    30. \"\phantom{1}\"
      \n\"\dfrac{\sqrt{8n^2}}{\sqrt{10n}}\div \sqrt{2n} \\\"
      \n\"\dfrac{\sqrt{4n}}{\sqrt{5}}\Rightarrow \dfrac{2\sqrt{n}}{\sqrt{5}}\"<\/li>\n<\/ol>\n","protected":false},"author":727,"menu_order":80,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-1696","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1696","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":4,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1696\/revisions"}],"predecessor-version":[{"id":2981,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1696\/revisions\/2981"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1696\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=1696"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=1696"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=1696"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=1696"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}