Answer Key 9.4

  1. 12\sqrt{5\cdot 16}
    12\cdot 4 \sqrt{5}
    48\sqrt{5}
  2. -5\sqrt{10\cdot 15}
    -5\sqrt{150}
    -5\sqrt{25\cdot 6}\Rightarrow -25\sqrt{6}
  3. \sqrt{15\cdot 12\cdot m^2}
    \sqrt{3\cdot 5\cdot 3\cdot 4\cdot m^2}
    3\cdot 2m\sqrt{5}
    6m\sqrt{5}
  4. -5\sqrt{5r^3\cdot 10r^2}
    -5\sqrt{25\cdot 2\cdot r^4\cdot r}
    -25r^2\sqrt{2r}
  5. \sqrt[3]{8x^7}
    \sqrt[3]{8\cdot x^6\cdot x}
    2x^2 \sqrt[3]{x}
  6. 3 \sqrt[3]{40a^7}
    3 \sqrt[3]{5\cdot 8\cdot a^6\cdot a}
    3\cdot 2a^2 \sqrt[3]{5a}\Rightarrow 6a^2 \sqrt[3]{5a}
  7. \sqrt{12}+2\sqrt{6}
    \sqrt{4\cdot 3}+2\sqrt{6}
    2\sqrt{3}+2\sqrt{6}
  8. \sqrt{50}+\sqrt{20}
    \sqrt{25\cdot 2}+\sqrt{4\cdot 5}
    5\sqrt{2}+2\sqrt{5}
  9. -15\sqrt{45}-10\sqrt{15}
    -15\sqrt{9\cdot 5}-10\sqrt{15}
    -15\cdot 3\sqrt{5}-10\sqrt{15}
    -45\sqrt{5}-10\sqrt{15}
  10. 15\sqrt{45}+10\sqrt{15}
    15\sqrt{9\cdot 5}+10\sqrt{15}
    15\cdot 3\sqrt{5}+10\sqrt{15}
    45\sqrt{5}+10\sqrt{15}
  11. 25n\sqrt{10}+5\sqrt{20}
    25n\sqrt{10}+5\sqrt{4\cdot 5}
    25n\sqrt{10}+10\sqrt{5}
  12. \sqrt{75}-3\sqrt{45v}
    \sqrt{25\cdot 3}-3\sqrt{9\cdot 5v}
    5\sqrt{3}-9\sqrt{5v}
  13. -6+2\sqrt{2}-6\sqrt{2}+2(\sqrt{2})(\sqrt{2})
    -6+2\sqrt{2}-6\sqrt{2}+2(2)
    -6+4+2\sqrt{2}-6\sqrt{2}
    -2-4\sqrt{2}
  14. 10-4\sqrt{3}-5\sqrt{3}+2(\sqrt{3})(\sqrt{3})
    10-4\sqrt{3}-5\sqrt{3}+2(3)
    10+6-4\sqrt{3}-5\sqrt{3}
    16-9\sqrt{3}
  15. (2\sqrt{5})(\sqrt{5})-\sqrt{5}-10\sqrt{5}+5
    2(5)-\sqrt{5}-10\sqrt{5}+5
    10+5-\sqrt{5}-10\sqrt{5}
    15-11\sqrt{5}
  16. 10(3)+4\sqrt{12}+5\sqrt{15}+2\sqrt{20}
    30+4\sqrt{4\cdot 3}+5\sqrt{15}+2\sqrt{5\cdot 4}
    30+5\sqrt{15}+8\sqrt{3}+4\sqrt{5}
  17. 3(2a)+6\sqrt{6a^2}+\sqrt{10a^2}+2\sqrt{15a^2}
    6a+6a\sqrt{6}+a\sqrt{10}+2a\sqrt{15}
  18. (-2\sqrt{2p}+5\sqrt{5})(2\sqrt{5p})
    -4\sqrt{10p^2}+10\sqrt{25p}
    -4p\sqrt{10}+50\sqrt{p}
  19. 15+12\sqrt{3}+20\sqrt{3}+16(3)
    63+32\sqrt{3}
  20. -5\sqrt{4m}+\sqrt{2m}+25\sqrt{2}-5
    -10\sqrt{m}+\sqrt{2m}+25\sqrt{2}-5
  21. \phantom{1}
    \dfrac{\sqrt{12}}{5\sqrt{100}}\div \sqrt{4} \\
    \dfrac{\sqrt{3}}{5\sqrt{25}}\Rightarrow \dfrac{\sqrt{3}}{5\cdot 5}\Rightarrow \dfrac{\sqrt{3}}{25}
  22. \dfrac{\sqrt{15}}{2\cdot 2}\Rightarrow \dfrac{\sqrt{15}}{4}
  23. \phantom{1}
    \dfrac{\sqrt{5}}{4\sqrt{125}}\div \sqrt{5} \\
    \dfrac{\sqrt{1}}{4\sqrt{25}}\Rightarrow \dfrac{1}{4\cdot 5}\Rightarrow \dfrac{1}{20}
  24. \phantom{1}
    \dfrac{\sqrt{12}}{\sqrt{3}}\div \sqrt{3} \\
    \dfrac{\sqrt{4}}{\sqrt{1}}\Rightarrow \dfrac{2}{1}\Rightarrow 2
  25. \phantom{1}
    \dfrac{\sqrt{10}}{\sqrt{6}}\div \sqrt{2} \\
    \dfrac{\sqrt{5}}{\sqrt{3}}
  26. Does not reduce
  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}}
  28. \dfrac{4}{5y^2\sqrt{3x}}
  29. \phantom{1}
    \dfrac{\sqrt{2p^2}}{\sqrt{3p}}\div \sqrt{p} \\
    \dfrac{\sqrt{2p}}{\sqrt{3}}
  30. \phantom{1}
    \dfrac{\sqrt{8n^2}}{\sqrt{10n}}\div \sqrt{2n} \\
    \dfrac{\sqrt{4n}}{\sqrt{5}}\Rightarrow \dfrac{2\sqrt{n}}{\sqrt{5}}

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Intermediate Algebra by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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