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Building Skills

9. 8
10. 10
11. 4
12. 5
13. $- 3$ $- 3$
14. $- 6$ $- 6$
15. $- \frac{1}{2}$ $- \frac{1}{2}$
16. $\frac{3}{4}$ $\frac{3}{4}$
17. 3
18. $- 6$ $- 6$
19. Not a real number
20. Not a real number
21. 1
22. $- 1$ $- 1$
23. $- 7$ $- 7$
24. 4
25. $4 \sqrt{2}$ $4 \sqrt{2}$
26. $5 \sqrt{5}$ $5 \sqrt{5}$
27. $3 x \sqrt{2}$ $3 x \sqrt{2}$
28. $3 x \sqrt{3}$ $3 x \sqrt{3}$
29. $3 x \sqrt{x}$ $3 x \sqrt{x}$
30. $2 x \sqrt{2 x}$ $2 x \sqrt{2 x}$
31. $3 x \sqrt{2}$ $3 x \sqrt{2}$
32. $5 x \sqrt{2}$ $5 x \sqrt{2}$
33. $3 x \sqrt{5 x}$ $3 x \sqrt{5 x}$
34. $6 x \sqrt{x}$ $6 x \sqrt{x}$
35. $- 2 x$ $- 2 x$
36. $4 x$ $4 x$
37. $- x^{2}$ $- x^{2}$
38. $- 3 x^{2}$ $- 3 x^{2}$
39. $\frac{\sqrt{10}}{8}$ $\frac{\sqrt{10}}{8}$
40. $\frac{\sqrt{6}}{10}$ $\frac{\sqrt{6}}{10}$
41. $\frac{2}{x}$ $\frac{2}{x}$
42. $\frac{\sqrt[3]{7}}{2 x}$ $\frac{\sqrt[3]{7}}{2 x}$
43. $\frac{\sqrt[4]{2 x^{3}}}{x^{2}}$ $\frac{\sqrt[4]{2 x^{3}}}{x^{2}}$
44. $- \frac{\sqrt[4]{5 x^{3}}}{2 x^{2}}$ $- \frac{\sqrt[4]{5 x^{3}}}{2 x^{2}}$
45. $x^{2}$ $x^{2}$
46. $\frac{2 x^{2}}{5 y^{3}}$ $\frac{2 x^{2}}{5 y^{3}}$
47. $\frac{3 x^{3}}{y^{2}}$ $\frac{3 x^{3}}{y^{2}}$
48. $x^{3} y$ $x^{3} y$
49. $7 \sqrt{3}$ $7 \sqrt{3}$
50. $6 \sqrt{2}$ $6 \sqrt{2}$
51. $9 \sqrt{5}$ $9 \sqrt{5}$
52. $6 \sqrt{7}$ $6 \sqrt{7}$
53. $3 \sqrt{2 x}$ $3 \sqrt{2 x}$
54. $5 \sqrt{5 x}$ $5 \sqrt{5 x}$
55. $- \sqrt[3]{3}$ $- \sqrt[3]{3}$
56. $5 \sqrt[3]{2}$ $5 \sqrt[3]{2}$
57. $2 \sqrt[3]{3 x}$ $2 \sqrt[3]{3 x}$
58. $10 \sqrt[3]{2 x}$ $10 \sqrt[3]{2 x}$
59. $\sqrt{2 x} (x^{2} + 3 x - 20)$ $\sqrt{2 x} (x^{2} + 3 x - 20)$
60. $\sqrt{2 x} (10 x^{2} + 7 x - 18)$ $\sqrt{2 x} (10 x^{2} + 7 x - 18)$
61. ${(2 x - y)}^{2} \sqrt{3 x y}$ ${(2 x - y)}^{2} \sqrt{3 x y}$
62. $\sqrt{2 x y} (2 x + 4 y - 3 x^{2})$ $\sqrt{2 x y} (2 x + 4 y - 3 x^{2})$
63. $\frac{2 \sqrt{3}}{3}$ $\frac{2 \sqrt{3}}{3}$
64. $2 \sqrt{5}$ $2 \sqrt{5}$
65. $\frac{7 \sqrt{15}}{15}$ $\frac{7 \sqrt{15}}{15}$
66. $- \frac{3 \sqrt{2}}{4}$ $- \frac{3 \sqrt{2}}{4}$
67. $\frac{\sqrt{2} - x}{2 - x^{2}}$ $\frac{\sqrt{2} - x}{2 - x^{2}}$
68. $\frac{\sqrt{5} - 2 x}{5 - 4 x^{2}}$ $\frac{\sqrt{5} - 2 x}{5 - 4 x^{2}}$
69. $3 (2 + \sqrt{3})$ $3 (2 + \sqrt{3})$
70. $5 (1 + \sqrt{2})$ $5 (1 + \sqrt{2})$
71. $\sqrt{3} - \sqrt{2}$ $\sqrt{3} - \sqrt{2}$
72. $3 (\sqrt{5} + \sqrt{3})$ $3 (\sqrt{5} + \sqrt{3})$
73. $\frac{7 - 2 \sqrt{10}}{3}$ $\frac{7 - 2 \sqrt{10}}{3}$
74. $\frac{5 + \sqrt{21}}{2}$ $\frac{5 + \sqrt{21}}{2}$
75. $\frac{2 x + h - 2 \sqrt{x (x + h)}}{h}$ $\frac{2 x + h - 2 \sqrt{x (x + h)}}{h}$
76. $\frac{a^{2} x + 6 a \sqrt{x} + 9}{a^{2} x - 9}$ $\frac{a^{2} x + 6 a \sqrt{x} + 9}{a^{2} x - 9}$
77. $\frac{1}{\sqrt{4 + h} + 2}$ $\frac{1}{\sqrt{4 + h} + 2}$
78. $\frac{1}{\sqrt{y + 9} + 3}$ $\frac{1}{\sqrt{y + 9} + 3}$
79. $\frac{1}{2 + \sqrt{4 - x}}$ $\frac{1}{2 + \sqrt{4 - x}}$
80. $\frac{1}{\sqrt{x + 2} + \sqrt{2}}$ $\frac{1}{\sqrt{x + 2} + \sqrt{2}}$
81. $\frac{1}{\sqrt{x} + 2}$ $\frac{1}{\sqrt{x} + 2}$
82. $\frac{1}{(x + 5) (\sqrt{x} + \sqrt{5})}$ $\frac{1}{(x + 5) (\sqrt{x} + \sqrt{5})}$
83. $\frac{2 x}{\sqrt{x^{2} + 4 x} + x}$ $\frac{2 x}{\sqrt{x^{2} + 4 x} + x}$
84. $\frac{x}{\sqrt{x^{2} + 2 x + 3} + \sqrt{x^{2} + 3}}$ $\frac{x}{\sqrt{x^{2} + 2 x + 3} + \sqrt{x^{2} + 3}}$
85. 5
86. 12
87. $- 2$ $- 2$
88. $- 3$ $- 3$
89. 4
90. 64
91. $- \frac{1}{125}$ $- \frac{1}{125}$
92. $- \frac{1}{27}$ $- \frac{1}{27}$
93. $\frac{125}{27}$ $\frac{125}{27}$
94. 9
95. $x^{9 / 10}$ $x^{9 / 10}$
96. $5 x^{19 / 15}$ $5 x^{19 / 15}$
97. $x^{1 / 10}$ $x^{1 / 10}$
98. $x^{11 / 12}$ $x^{11 / 12}$
99. $4 x^{4}$ $4 x^{4}$
100. $4 x^{3 / 2}$ $4 x^{3 / 2}$
101. $\frac{1}{9 x^{4} y^{2}}$ $\frac{1}{9 x^{4} y^{2}}$
102. $\frac{1}{64 x^{6} y^{9}}$ $\frac{1}{64 x^{6} y^{9}}$
103. $5 x^{5 / 4}$ $5 x^{5 / 4}$
104. $5 x^{11 / 6}$ $5 x^{11 / 6}$
105. $\frac{x^{3}}{y^{8}}$ $\frac{x^{3}}{y^{8}}$
106. $\frac{x^{5 / 6}}{3 y}$ $\frac{x^{5 / 6}}{3 y}$
107. $3^{1 / 2}$ $3^{1 / 2}$
108. $5^{1 / 2}$ $5^{1 / 2}$
109. $x^{3}$ $x^{3}$
110. $x^{4}$ $x^{4}$
111. $x^{2} y^{3}$ $x^{2} y^{3}$
112. $2 x y^{4}$ $2 x y^{4}$
113. 3
114. 7
115. $x^{5 / 3}$ $x^{5 / 3}$
116. 2x
117. $\sqrt[15]{864}$ $\sqrt[15]{864}$
118. $\sqrt[12]{648}$ $\sqrt[12]{648}$
119. $x (\sqrt[12]{x^{5}})$ $x (\sqrt[12]{x^{5}})$
120. $x (\sqrt[35]{x^{4}})$ $x (\sqrt[35]{x^{4}})$
121. $m \sqrt[9]{250 m^{8} n^{7}}$ $m \sqrt[9]{250 m^{8} n^{7}}$
122. $3 x y (\sqrt[6]{3 x y})$ $3 x y (\sqrt[6]{3 x y})$
123. $x y (\sqrt[30]{x^{9} y^{13}})$ $x y (\sqrt[30]{x^{9} y^{13}})$
124. $a b \sqrt[30]{3^{6} 7^{5} a^{4} b^{12}}$ $a b \sqrt[30]{3^{6} 7^{5} a^{4} b^{12}}$
125. $\frac{2}{3} x^{1 / 3} (7 x - 6)$ $\frac{2}{3} x^{1 / 3} (7 x - 6)$
126. $\frac{1}{3} x^{1 / 3} (49 x + 4)$ $\frac{1}{3} x^{1 / 3} (49 x + 4)$
127. $2 {(3 x + 1)}^{1 / 3} (7 x - 1)$ $2 {(3 x + 1)}^{1 / 3} (7 x - 1)$
128. $7 {(3 x - 1)}^{1 / 3} (x + 1)$ $7 {(3 x - 1)}^{1 / 3} (x + 1)$
129. ${(x^{2} + 1)}^{1 / 2} (14 x^{3} - 5 x^{2} + 8 x - 2)$ ${(x^{2} + 1)}^{1 / 2} (14 x^{3} - 5 x^{2} + 8 x - 2)$
130. ${(x^{2} + 2)}^{1 / 2} (5 x^{3} - 8 x^{2} + 4 x - 4)$ ${(x^{2} + 2)}^{1 / 2} (5 x^{3} - 8 x^{2} + 4 x - 4)$

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Table of Contents for Building Skills

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Table of Contents for
Building Skills