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Exercises 11.5, page 341

1. $3 \sqrt{10} - 16$ $3 \sqrt{10} - 16$
3. $\sqrt{3} - \sqrt{2}$ $\sqrt{3} - \sqrt{2}$
5. $\sqrt{35}$ $\sqrt{35}$
7. $2 \sqrt{3}$ $2 \sqrt{3}$
9. 2
11. 48
13. $6 \sqrt{5}$ $6 \sqrt{5}$
15. $3 \sqrt{2} - \sqrt{15}$ $3 \sqrt{2} - \sqrt{15}$
17. $- 1$ $- 1$
19. $- 12 + 15 \sqrt{10}$ $- 12 + 15 \sqrt{10}$
21. $66 + 13 \sqrt{11 x} - 5 x$ $66 + 13 \sqrt{11 x} - 5 x$
23. $a \sqrt{b} + c \sqrt{a c}$ $a \sqrt{b} + c \sqrt{a c}$
25. $\frac{2 - 3 \sqrt{6}}{2}$ $\frac{2 - 3 \sqrt{6}}{2}$
27. $x - 8 \sqrt{x y} + 16 y$ $x - 8 \sqrt{x y} + 16 y$
29. $2 a - 3 b + 2 \sqrt{2 a b}$ $2 a - 3 b + 2 \sqrt{2 a b}$
31. $\sqrt[6]{72}$ $\sqrt[6]{72}$
33. $\frac{1}{4} (\sqrt{7} - \sqrt{3})$ $\frac{1}{4} (\sqrt{7} - \sqrt{3})$
35. $\frac{1}{11} (\sqrt{7} + 3 \sqrt{2} - 6 - \sqrt{14})$ $\frac{1}{11} (\sqrt{7} + 3 \sqrt{2} - 6 - \sqrt{14})$
37. $\frac{1}{17} (- 56 + 9 \sqrt{15})$ $\frac{1}{17} (- 56 + 9 \sqrt{15})$
39. $\frac{6 x + 6 \sqrt{5 x}}{x - 5}$ $\frac{6 x + 6 \sqrt{5 x}}{x - 5}$
41. 1
43. $\frac{2 - R - R^{2}}{R}$ $\frac{2 - R - R^{2}}{R}$
45. $- \frac{\sqrt{x^{2} - y^{2}} + \sqrt{x^{2} + x y}}{y}$ $- \frac{\sqrt{x^{2} - y^{2}} + \sqrt{x^{2} + x y}}{y}$
47. $a - 1 + \sqrt{a (a - 2)}$ $a - 1 + \sqrt{a (a - 2)}$
49. $- 1 - \sqrt{66} = - 9.1240384$ $- 1 - \sqrt{66} = - 9.1240384$
51. $- \frac{16 + 5 \sqrt{30}}{26} = - 1.6686972$ $- \frac{16 + 5 \sqrt{30}}{26} = - 1.6686972$
53. $\frac{2 x + 1}{\sqrt{x}}$ $\frac{2 x + 1}{\sqrt{x}}$
55. $\frac{5 x^{2} + 2 x}{\sqrt{2 x + 1}}$ $\frac{5 x^{2} + 2 x}{\sqrt{2 x + 1}}$
57. $\frac{- 1}{5 \sqrt{2} - 4 \sqrt{5}}$ $\frac{- 1}{5 \sqrt{2} - 4 \sqrt{5}}$
59. $\frac{1}{\sqrt{x + h} + \sqrt{x}}$ $\frac{1}{\sqrt{x + h} + \sqrt{x}}$
61. Yes — if either x or y is zero and the other is $\geq 0.$ $\geq 0.$
63.
$\begin{array}{l} {(1 - \sqrt{2})}^{2} - 2 (1 - \sqrt{2}) - 1 \\ = 1 - 2 \sqrt{2} + 2 - 2 + 2 \sqrt{2} - 1 = 0 \end{array}$ $\begin{array}{l} {(1 - \sqrt{2})}^{2} - 2 (1 - \sqrt{2}) - 1 \\ = 1 - 2 \sqrt{2} + 2 - 2 + 2 \sqrt{2} - 1 = 0 \end{array}$
65. $a = c$ $a = c$
67. $\frac{\sqrt[3]{x} - 1}{x - 1}$ $\frac{\sqrt[3]{x} - 1}{x - 1}$
69.

$\begin{array}{l} {[\frac{1}{2} (\sqrt{b^{2} - 4 k^{2}} - b)]}^{2} + b [\frac{1}{2} (\sqrt{b^{2} - 4 k^{2}} - b)] + k^{2} \\ = \frac{1}{4} (b^{2} - 4 k^{2}) - \frac{b}{2} \sqrt{b^{2} - 4 k^{2}} + \frac{1}{4} b^{2} \\ + \frac{b}{2} \sqrt{b^{2} - 4 k^{2}} - \frac{1}{2} b^{2} + k^{2} = 0 \end{array}$ $\begin{array}{l} {[\frac{1}{2} (\sqrt{b^{2} - 4 k^{2}} - b)]}^{2} + b [\frac{1}{2} (\sqrt{b^{2} - 4 k^{2}} - b)] + k^{2} \\ = \frac{1}{4} (b^{2} - 4 k^{2}) - \frac{b}{2} \sqrt{b^{2} - 4 k^{2}} + \frac{1}{4} b^{2} \\ + \frac{b}{2} \sqrt{b^{2} - 4 k^{2}} - \frac{1}{2} b^{2} + k^{2} = 0 \end{array}$
71. $\frac{2500 - 50 \sqrt{V}}{2500 - V}$ $\frac{2500 - 50 \sqrt{V}}{2500 - V}$
73. $2 Q \sqrt{\sqrt{2} + 1}$ $2 Q \sqrt{\sqrt{2} + 1}$
75. $\frac{\sqrt{L C - R^{2} C^{2}}}{L C}$ $\frac{\sqrt{L C - R^{2} C^{2}}}{L C}$

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Table of Contents for Exercises 11.5, page 341

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Table of Contents for
Exercises 11.5, page 341