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Practice and Applications

7. $\frac{8}{x^{3}}$ $\frac{8}{x^{3}}$
9. $\frac{9 d^{3}}{c}$ $\frac{9 d^{3}}{c}$
11. 375
13. $\frac{1}{1000}$ $\frac{1}{1000}$
15. $\frac{t^{4}}{9}$ $\frac{t^{4}}{9}$
17. $- 28$ $- 28$
19. $64 a^{4} b$ $64 a^{4} b$
21. $- 8 m^{9} n^{6}$ $- 8 m^{9} n^{6}$
23. $\frac{6 C - 4 L^{2}}{C L^{2}}$ $\frac{6 C - 4 L^{2}}{C L^{2}}$
25. $\frac{3 y}{x + 3 y}$ $\frac{3 y}{x + 3 y}$
27. $\frac{b}{a b - 3}$ $\frac{b}{a b - 3}$
29. $\frac{{(x^{3} y^{3} - 1)}^{1/3}}{y}$ $\frac{{(x^{3} y^{3} - 1)}^{1/3}}{y}$
31. $\frac{1}{W - H}$ $\frac{1}{W - H}$
33. $\frac{- 2 (x + 1)}{{(x - 1)}^{3}}$ $\frac{- 2 (x + 1)}{{(x - 1)}^{3}}$
35. $2 \sqrt{15}$ $2 \sqrt{15}$
37. $b^{2} c \sqrt{a b}$ $b^{2} c \sqrt{a b}$
39. $3 a b^{2} \sqrt{a}$ $3 a b^{2} \sqrt{a}$
41. $\frac{2 t \sqrt{21 s t}}{u}$ $\frac{2 t \sqrt{21 s t}}{u}$
43. $\frac{5 \sqrt{2 s}}{2 s}$ $\frac{5 \sqrt{2 s}}{2 s}$
45. $\frac{2 \sqrt{6}}{9}$ $\frac{2 \sqrt{6}}{9}$
47. $m n^{2} \sqrt[4]{8 m^{2} n}$ $m n^{2} \sqrt[4]{8 m^{2} n}$
49. $\sqrt{2}$ $\sqrt{2}$
51. 0
53. $- 7 \sqrt{7}$ $- 7 \sqrt{7}$
55. $3 a x \sqrt{2 x}$ $3 a x \sqrt{2 x}$
57. $(2 a + b) \sqrt[3]{a}$ $(2 a + b) \sqrt[3]{a}$
59. $150 - 25 \sqrt{7}$ $150 - 25 \sqrt{7}$
61. $4 \sqrt{3} - 4 \sqrt{5}$ $4 \sqrt{3} - 4 \sqrt{5}$
63. $6 - 51 B - 7 \sqrt{17 B}$ $6 - 51 B - 7 \sqrt{17 B}$
65. $42 - 7 \sqrt{7 a} - 3 a$ $42 - 7 \sqrt{7 a} - 3 a$
67. $36 x - 48 \sqrt{x y} + 16 y$ $36 x - 48 \sqrt{x y} + 16 y$
69. $\frac{6 x + \sqrt{3 x y}}{12 x - y}$ $\frac{6 x + \sqrt{3 x y}}{12 x - y}$
71. $- \frac{8 + \sqrt{6}}{29}$ $- \frac{8 + \sqrt{6}}{29}$
73. $\frac{13 - 2 \sqrt{35}}{29}$ $\frac{13 - 2 \sqrt{35}}{29}$
75. $\frac{6 x - 13 a \sqrt{x} + 5 a^{2}}{9 x - 25 a^{2}}$ $\frac{6 x - 13 a \sqrt{x} + 5 a^{2}}{9 x - 25 a^{2}}$
77. $\sqrt{4 b^{2} + 1}$ $\sqrt{4 b^{2} + 1}$
79. $9 x - 4 x^{2}$ $9 x - 4 x^{2}$
81. $1 + 6^{1/2}$ $1 + 6^{1/2}$
83. $\frac{15 - 2 \sqrt{15}}{4}$ $\frac{15 - 2 \sqrt{15}}{4}$
85. $51 - 7 \sqrt{105} = - 20.728655$ $51 - 7 \sqrt{105} = - 20.728655$
87.

$\begin{array}{l} \sqrt{\sqrt{2} - 1} (\sqrt{2} + 1) = \sqrt{(\sqrt{2} - 1) {(\sqrt{2} + 1)}^{2}} \\ = \sqrt{(\sqrt{2} - 1) (3 + 2 \sqrt{2})} = \sqrt{\sqrt{2} + 1} = 1.5537740 \end{array}$ $\begin{array}{l} \sqrt{\sqrt{2} - 1} (\sqrt{2} + 1) = \sqrt{(\sqrt{2} - 1) {(\sqrt{2} + 1)}^{2}} \\ = \sqrt{(\sqrt{2} - 1) (3 + 2 \sqrt{2})} = \sqrt{\sqrt{2} + 1} = 1.5537740 \end{array}$
89. $12 \sqrt{2}$ $12 \sqrt{2}$
91. $\frac{33}{4} - 2 \sqrt{3}$ $\frac{33}{4} - 2 \sqrt{3}$
93. 1.676%
95.
1. $v = k {(P / W)}^{1/3}$ $v = k {(P / W)}^{1/3}$
2. $v = \frac{k \sqrt[3]{P W^{2}}}{W}$ $v = \frac{k \sqrt[3]{P W^{2}}}{W}$
97. $\frac{100 (1 + 2 \sqrt{x})}{x}$ $\frac{100 (1 + 2 \sqrt{x})}{x}$
99. $\frac{c}{{(c^{2} - v^{2})}^{1/2}}$ $\frac{c}{{(c^{2} - v^{2})}^{1/2}}$
101. $\frac{1}{\sqrt{A + h} + \sqrt{A}}$ $\frac{1}{\sqrt{A + h} + \sqrt{A}}$
103. $6 \sqrt{2} cm$ $6 \sqrt{2} cm$
105. $\frac{\sqrt{L C_{1} C_{2} (C_{1} + C_{2})}}{2 π L C_{1} C_{2}}$ $\frac{\sqrt{L C_{1} C_{2} (C_{1} + C_{2})}}{2 π L C_{1} C_{2}}$

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Table of Contents for Practice and Applications

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Table of Contents for
Practice and Applications