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\cl {\bf Numbers and Their Application to Math and Science}
\cl {\bf Homework for Numbers Lesson 10}

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{\bf Simplifying Square Roots}\hb
$\sqrt{75}=\sqrt{25\cdot3}=\sqrt{25}\cdot\sqrt{3}=5\sqrt{3}$\hb
$\sqrt{76}=\sqrt{4\cdot19}=\sqrt{4}\sqrt{19}=2\sqrt{19}$\hb
$\sqrt{144}=\sqrt{9\cdot16}=\sqrt{9}\sqrt{16}=3\cdot4=12$\hfill
        $\sqrt{54}=\sqrt{9\cdot6}=\sqrt{9}\sqrt{6}=3\sqrt{6}$ not $3\sqrt{2}\sqrt{3}$
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{\bf Multiplying Square Roots}\hb
$(\sqrt{3})(\sqrt{2})=(\sqrt{6})$\hb
$(\sqrt{3})^2=(\sqrt{3})(\sqrt{3})=3$\hb
$(2\sqrt{3})^2=(2\sqrt{3})(2\sqrt{3})=4\cdot3=12$
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{\bf Rationalizing the Denominator}\hb
$\sqrt{2\over3}={\sqrt{2}\over\sqrt{3}}={\sqrt{2}\over\sqrt{3}}\cdot
                              {\sqrt{3}\over\sqrt{3}}={\sqrt{6}\over3}$\hb
$\sqrt{3\over8}={\sqrt{3}\over\sqrt{8}}={\sqrt{3}\over\sqrt{8}}\cdot
                              {\sqrt{2}\over\sqrt{2}}={\sqrt{6}\over\sqrt{16}}=
                              {\sqrt{6}\over4}$

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{\bf Express each square root EXACTLY in simplest form.}

1. $\sqrt{12}$\hfill  2. $\sqrt{18}$\hfill  3. $\sqrt{24}$\hfill  4. $\sqrt{32}$\hfill  5. $\sqrt{40}$
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6. $\sqrt{48}$\hfill  7. $\sqrt{60}$\hfill  8. $\sqrt{75}$\hfill  9. $\sqrt{73}$\hfill  10. $\sqrt{95}$
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11. $\sqrt{90}$\hfill 12. $\sqrt{216}$\hfill 13. $\sqrt{120}$\hfill 14. $\sqrt{235}$\hfill 15. $\sqrt{810}$
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16. $\sqrt{324}$\hfill 17. $\sqrt{720}$\hfill 18. $\sqrt{242}$\hfill 19. $\sqrt{784}$\hfill 20. $\sqrt{828}$
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{\bf Express each product EXACTLY in simplest form.}

21. $(3\sqrt{2})^2$\hfill 22. $(4\sqrt{3})^2$\hfill 23. $(2\sqrt{3})(\sqrt{2})$\hfill
                         24. $(3\sqrt{6})(2\sqrt{3})$\hfill 25. $(7\sqrt{3})^2$
                         
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{\bf Rationalize the denominator, then simplify EXACTLY.}

26. $\sqrt{1\over3}$\hfill 27. $\sqrt{5\over24}$\hfill 28. $\sqrt{7\over27}$\hfill
                          29. $\sqrt{35\over50}$\hfill 30. $\sqrt{1\over2}$
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\noindent%
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Copyright \copyright 1999--2005, Keith G. Calkins. Revised on or after September 16, 2005.
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