Lynn Marecek; MaryAnne Anthony-Smith

Chapter 9

Try It

9.1

ⓐ $−7$ ⓑ $15$

9.2

ⓐ $8$ ⓑ $−11$

9.3

ⓐ not a real number ⓑ $−9$

9.4

ⓐ $−7$ ⓑ not a real number

9.5

ⓐ 7 ⓑ 5

9.6

ⓐ 17 ⓑ $23$

9.7

$6 < \sqrt{38} < 7$

9.8

$9 < \sqrt{84} < 10$

9.9

$\approx 3.32$

9.10

$\approx 3.61$

9.11

ⓐ $y^{4}$ ⓑ $z^{6}$

9.12

ⓐ $m^{2}$ ⓑ $b^{5}$

9.13

$8 x$

9.14

$13 y$

9.15

$−11 y$

9.16

$−10 p$

9.17

$10 a b$

9.18

$15 m n$

9.19

$7 x^{15}$

9.20

$9 w^{18}$

9.21

$13 x^{5} y^{7}$

9.22

$12 p^{6} q^{10}$

9.23

$4 \sqrt{3}$

9.24

$3 \sqrt{5}$

9.25

$12 \sqrt{2}$

9.26

$12 \sqrt{3}$

9.27

$b^{2} \sqrt{b}$

9.28

$p^{4} \sqrt{p}$

9.29

$4 x^{3} \sqrt{x}$

9.30

$7 v^{4} \sqrt{v}$

9.31

$4 y^{2} \sqrt{2 y}$

9.32

$5 a^{4} \sqrt{3 a}$

9.33

$7 a^{3} b^{2} {\sqrt{2 a b}}^{}$

9.34

$6 m^{4} n^{5} \sqrt{5 m n}$

9.35

$5 + 5 \sqrt{3}$

9.36

$2 + 7 \sqrt{2}$

9.37

$2 - \sqrt{3}$

9.38

$2 - \sqrt{5}$

9.39

$\frac{5}{4}$

9.40

$\frac{7}{9}$

9.41

$\frac{5}{4}$

9.42

$\frac{7}{9}$

9.43

$a$

9.44

$x^{2}$

9.45

$5 x^{2}$

9.46

$6 z$

9.47

$\frac{\sqrt{19}}{7}$

9.48

$\frac{2 \sqrt{7}}{9}$

9.49

$\frac{2 p \sqrt{6 p}}{7}$

9.50

$\frac{2 x^{2} \sqrt{3 x}}{5}$

9.51

$\frac{4 m \sqrt{5 m}}{n^{3}}$

9.52

$\frac{3 u^{3} \sqrt{6 u}}{v^{4}}$

9.53

$\frac{8 x^{2}}{3}$

9.54

$\frac{2 a^{2}}{5}$

9.55

$\frac{5 y \sqrt{x}}{6}$

9.56

$\frac{4 m \sqrt{3}}{5 n^{3} \sqrt{5 n}}$

9.57

$− \sqrt{2}$

9.58

$−4 \sqrt{3}$

9.59

$9 \sqrt{x}$

9.60

$8 \sqrt{u}$

9.61

$7 \sqrt{p} - 6 \sqrt{q}$

9.62

$6 \sqrt{a} - 3 \sqrt{b}$

9.63

$9 \sqrt{11}$

9.64

$11 \sqrt{10}$

9.65

$\sqrt{5} + 2 \sqrt{6}$

9.66

$−5 \sqrt{7} + 2 \sqrt{5}$

9.67

$−2 \sqrt{7 x}$

9.68

$− \sqrt{3 y}$

9.69

$−2 \sqrt{5 x y}$

9.70

$0$

9.71

$9 \sqrt{2}$

9.72

$7 \sqrt{3}$

9.73

$\sqrt{2}$

9.74

$− \sqrt{5}$

9.75

$6 \sqrt{3}$

9.76

$−15 \sqrt{5}$

9.77

$− \sqrt{3}$

9.78

$0$

9.79

$\frac{14}{15} \sqrt{2}$

9.80

$\frac{1}{12} \sqrt{5}$

9.81

$− m^{3} \sqrt{2 m}$

9.82

$− p \sqrt{3 p}$

9.83

$20 x \sqrt{2} - 12 x \sqrt{3}$

9.84

$28 y \sqrt{3} - 24 y \sqrt{2}$

9.85

$10 x \sqrt{3}$

9.86

$−5 x \sqrt{2}$

9.87

ⓐ $3 \sqrt{2}$ ⓑ $36 \sqrt{2}$

9.88

ⓐ $5 \sqrt{2}$ ⓑ $90 \sqrt{2}$

9.89

$12 \sqrt{15}$

9.90

$27 \sqrt{2}$

9.91

ⓐ $3 x^{2} \sqrt{2}$ ⓑ $10 y^{2} \sqrt{y}$

9.92

ⓐ $2 x^{3} \sqrt{3}$ ⓑ $6 y^{2} \sqrt{y}$

9.93

$144 x^{3} \sqrt{10}$

9.94

$144 y^{2} \sqrt{5 y}$

9.95

ⓐ 12 ⓑ $15$

9.96

ⓐ 16 ⓑ 20

9.97

ⓐ 330 ⓑ 200

9.98

ⓐ 210 ⓑ 96

9.99

ⓐ $6 - 2 \sqrt{5}$ ⓑ $2 \sqrt{3} - 3 \sqrt{6}$

9.100

ⓐ $12 + 6 \sqrt{6}$ ⓑ $\sqrt{7} + 7 \sqrt{2}$

9.101

ⓐ $18 + \sqrt{6}$ ⓑ $6 + 12 \sqrt{2}$

9.102

ⓐ $−40 + 4 \sqrt{2}$ ⓑ $2 \sqrt{7} + 14 \sqrt{3}$

9.103

$−3 + 2 \sqrt{6}$

9.104

$−2 + 2 \sqrt{10}$

9.105

$−66 + 15 \sqrt{7}$

9.106

$41 + 14 \sqrt{11}$

9.107

$1 + 9 \sqrt{21}$

9.108

$−12 - 20 \sqrt{3}$

9.109

$12 - 8 \sqrt{m} - 15 m$

9.110

$10 - 47 \sqrt{n} - 15 n$

9.111

ⓐ $102 + 20 \sqrt{2}$ ⓑ $55 + 6 \sqrt{6}$

9.112

ⓐ $31 - 12 \sqrt{5}$ ⓑ $121 - 36 \sqrt{10}$

9.113

$4 + 20 \sqrt{m} + 25 m$

9.114

$9 - 24 \sqrt{n} + 16 n$

9.115

$1$

9.116

$−4$

9.117

$−11$

9.118

$−159$

9.119

$\frac{\sqrt{2}}{2}$

9.120

$\frac{\sqrt{3}}{3}$

9.121

$\frac{4 - \sqrt{10}}{5}$

9.122

$\frac{5 - \sqrt{3}}{4}$

9.123

$\frac{2}{3}$

9.124

$\frac{4}{3}$

9.125

$n \sqrt{2}$

9.126

$p^{2} \sqrt{7}$

9.127

$\frac{5 s}{8}$

9.128

$\frac{5 q^{2}}{6}$

9.129

$\frac{9 x^{2}}{y^{2}}$

9.130

$\frac{10 n^{3}}{m}$

9.131

$\frac{5 \sqrt{3}}{3}$

9.132

$\frac{6 \sqrt{5}}{5}$

9.133

$\frac{\sqrt{5}}{2}$

9.134

$- \frac{3 \sqrt{3}}{4}$

9.135

$\frac{\sqrt{14}}{6}$

9.136

$\frac{\sqrt{6}}{8}$

9.137

$\frac{1}{3}$

9.138

$\frac{\sqrt{5}}{5}$

9.139

$\frac{2 (2 - \sqrt{3})}{1}$

9.140

$\frac{5 (5 - \sqrt{3})}{22}$

9.141

$- \frac{3 (1 + \sqrt{5})}{4}$

9.142

$\frac{4 + \sqrt{6}}{5}$

9.143

$\frac{\sqrt{5} (\sqrt{x} - \sqrt{2})}{x - 2}$

9.144

$\frac{\sqrt{10} (\sqrt{y} + \sqrt{3})}{y - 3}$

9.145

${\frac{(\sqrt{p} + \sqrt{2})}{p - 2}}^{2}$

9.146

${\frac{(\sqrt{q} - \sqrt{10})}{q - 10}}^{2}$

9.147

ⓐ no ⓑ $yes$

9.148

ⓐ no ⓑ $yes$

9.149

$10$

9.150

$7$

9.151

$\frac{23}{3}$

9.152

$\frac{3}{10}$

9.153

$\frac{1}{2}$

9.154

$\frac{3}{5}$

9.155

$no solution$

9.156

$no solution$

9.157

$2, 3$

9.158

$5, 6$

9.159

$7$

9.160

$3$

9.161

$\frac{127}{2}$

9.162

$\frac{311}{3}$

9.163

no solution

9.164

no solution

9.165

$no solution$

9.166

$no solution$

9.167

$no solution$

9.168

$no solution$

9.169

$19.2 yards$

9.170

$52.0 cm$

9.171

$9 seconds$

9.172

$3.5 seconds$

9.173

$42.7 feet$

9.174

$54.1 feet$

9.175

ⓐ 3 ⓑ 4 ⓒ 3

9.176

ⓐ 10 ⓑ 2 ⓒ 2

9.177

ⓐ $−5$ ⓑ not real ⓒ $−2$

9.178

ⓐ $−6$ ⓑ not real ⓒ $−4$

9.179

ⓐ $| b |$ ⓑ $w$ ⓒ $| m |$ ⓓ $q$

9.180

ⓐ $| y |$ ⓑ $p$ ⓒ $| z |$ ⓓ $q$

9.181

ⓐ $u^{3}$ ⓑ $v^{5}$

9.182

ⓐ $c^{4}$ ⓑ $d^{4}$

9.183

ⓐ $3 x^{9}$ ⓑ $3 | q^{7} |$

9.184

ⓐ $5 p^{3}$ ⓑ $3 q^{5}$

9.185

ⓐ $| y | \sqrt[4]{y^{2}}$ ⓑ $z \sqrt[3]{z^{2}}$

9.186

ⓐ $p \sqrt[5]{p^{3}}$ ⓑ $q^{2} \sqrt[6]{q}$

9.187

ⓐ $3 \sqrt[3]{4}$ ⓑ $2 \sqrt[4]{4}$

9.188

ⓐ $5 \sqrt[3]{5}$ ⓑ $3 \sqrt[4]{9}$

9.189

ⓐ $3 p^{3} \sqrt[3]{2 p}$ ⓑ $2 q^{2} \sqrt[4]{4 q^{2}}$

9.190

ⓐ $4 m^{3} \sqrt[3]{2 m^{2}}$ ⓑ $3 | n | \sqrt[4]{2 n^{3}}$

9.191

ⓐ $−3 \sqrt[3]{4}$ ⓑ $not real$

9.192

ⓐ $−5 \sqrt[3]{5}$ ⓑ $not real$

9.193

ⓐ $| x |$ ⓑ $y^{3}$

9.194

ⓐ $m^{2}$ ⓑ $n^{2}$

9.195

ⓐ $not real$ ⓑ $3 | m | \sqrt[4]{2 m^{2}}$

9.196

ⓐ $−4$ ⓑ $3 | n | \sqrt[4]{2}$

9.197

ⓐ $\frac{3 c^{3} \sqrt[3]{4 c}}{d^{2}}$ ⓑ $\frac{x^{2}}{| y |} \sqrt[4]{\frac{80 x^{2}}{y}}$

9.198

ⓐ $r \sqrt[3]{\frac{40}{s}}$ ⓑ $\frac{3 m^{3} \sqrt[4]{2 m^{2}}}{| n^{3} |}$

9.199

ⓐ $2 \sqrt[5]{3 x}$ ⓑ $2 \sqrt[3]{9}$

9.200

ⓐ $2 \sqrt[4]{10 y}$ ⓑ $2 \sqrt[6]{32}$

9.201

ⓐ $\sqrt[3]{3}$ ⓑ $6 \sqrt[4]{2}$

9.202

ⓐ $− \sqrt[3]{2}$ ⓑ $5 \sqrt[5]{2}$

9.203

ⓐ $2 y \sqrt[3]{4 y^{2}} + 3 y^{2} \sqrt[3]{4 y^{2}}$ ⓑ $3 r^{2} \sqrt[4]{3 r^{3}} + 4 r^{2} \sqrt[4]{3 r^{2}}$

9.204

ⓐ $2 z^{2} \sqrt[3]{5 z} + 3 z \sqrt[3]{5 z}$ ⓑ $2 | s^{3} | \sqrt[4]{5 s} + 4 | s | \sqrt[4]{5 s}$

9.205

ⓐ $\sqrt{t}$ ⓑ $\sqrt[3]{m}$ ⓒ $\sqrt[4]{r}$

9.206

ⓐ $\sqrt{b}$ ⓑ $\sqrt[3]{z}$ ⓒ $\sqrt[4]{p}$

9.207

ⓐ $s^{\frac{1}{2}}$ ⓑ $x^{\frac{1}{3}}$ ⓒ $b^{\frac{1}{4}}$

9.208

ⓐ $v^{\frac{1}{2}}$ ⓑ $p^{\frac{1}{3}}$ ⓒ $p^{\frac{1}{4}}$

9.209

ⓐ ${(10 m)}^{\frac{1}{2}}$ ⓑ ${(3 n)}^{\frac{1}{5}}$ ⓒ ${(486 y)}^{\frac{1}{4}}$

9.210

ⓐ ${(3 k)}^{\frac{1}{7}}$ ⓑ ${(5 j)}^{\frac{1}{4}}$ ⓒ ${(1024 a)}^{\frac{1}{3}}$

9.211

ⓐ 6 ⓑ 2 ⓒ 2

9.212

ⓐ 10 ⓑ 3 ⓒ 3

9.213

ⓐ $−5$ ⓑ $−5$ ⓒ $\frac{1}{5}$

9.214

ⓐ $−2$ ⓑ $−2$ ⓒ $\frac{1}{2}$

9.215

ⓐ $−8$ ⓑ $−8$ ⓒ $\frac{1}{8}$

9.216

ⓐ $−4$ ⓑ $−4$ ⓒ $\frac{1}{4}$

9.217

ⓐ $x^{\frac{5}{2}}$ ⓑ $z^{\frac{3}{4}}$ ⓒ $y^{\frac{2}{5}}$

9.218

ⓐ $a^{\frac{2}{5}}$ ⓑ $b^{\frac{7}{3}}$ ⓒ $m^{\frac{5}{4}}$

9.219

ⓐ 8 ⓑ 9 ⓒ 125

9.220

ⓐ 32 ⓑ 729 ⓒ 8

9.221

ⓐ $\frac{1}{32}$ ⓑ $\frac{1}{729}$ ⓒ $\frac{1}{8}$

9.222

ⓐ $\frac{1}{8}$ ⓑ $\frac{1}{9}$ ⓒ $\frac{1}{125}$

9.223

ⓐ $−64$ ⓑ $- \frac{1}{64}$ ⓒ not a real number

9.224

ⓐ $−729$ ⓑ $- \frac{1}{729}$ ⓒ not a real number

9.225

ⓐ 9 ⓑ $y^{3}$ ⓒ m

9.226

ⓐ 25 ⓑ z ⓒ n

9.227

ⓐ $p^{2}$ ⓑ $q^{6}$ ⓒ $x^{8}$

9.228

ⓐ $r^{10}$ ⓑ $s^{9}$ ⓒ $m^{2}$

9.229

ⓐ u ⓑ $v^{\frac{1}{5}}$ ⓒ $\frac{1}{x}$

9.230

ⓐ $c^{6}$ ⓑ $\frac{1}{m}$ ⓒ $\frac{1}{d}$

9.231

ⓐ $8 x^{\frac{1}{5}}$ ⓑ $4 y^{\frac{2}{9}}$

9.232

ⓐ $64 m^{\frac{1}{2}}$ ⓑ $729 n^{\frac{3}{5}}$

9.233

ⓐ $m^{2}$ ⓑ $n^{3}$

9.234

ⓐ $u^{3}$ ⓑ $v^{5}$

Section 9.1 Exercises

1.

6

3.

8

5.

3

7.

10

9.

$−2$

11.

$−1$

13.

not a real number

15.

not a real number

17.

5

19.

7

21.

$8 < \sqrt{70} < 9$

23.

$14 < \sqrt{200} < 15$

25.

4.36

27.

7.28

29.

$y$

31.

$a^{7}$

33.

$7 x$

35.

$11 m^{10}$

37.

$9 x^{18}$

39.

$−9 x^{9}$

41.

$−8 a$

43.

$12 x y$

45.

$13 w^{4} y^{5}$

47.

$3 c^{4} d^{6}$

49.

25 centimeters

51.

Answers will vary.

Section 9.2 Exercises

53.

$3 \sqrt{3}$

55.

$5 \sqrt{5}$

57.

$10 \sqrt{2}$

59.

$15 \sqrt{2}$

61.

$20 \sqrt{2}$

63.

$15 \sqrt{3}$

65.

$x^{3} \sqrt{x}$

67.

$p \sqrt{p}$

69.

$m^{6} \sqrt{m}$

71.

$r^{12} \sqrt{r}$

73.

$7 n^{8} \sqrt{n}$

75.

$9 r^{7} \sqrt{r}$

77.

$7 m^{2} \sqrt{2 m}$

79.

$5 r^{6} \sqrt{5 r}$

81.

$10 p^{6} \sqrt{2 p}$

83.

$11 m^{11} \sqrt{2 m}$

85.

$7 m^{3} n^{5} \sqrt{3 m n}$

87.

$5 r^{6} s^{4} \sqrt{3 r s}$ 70)

89.

$10 p^{4} q^{5} \sqrt{3 p q}$

91.

$11 m^{6} n^{10} \sqrt{2 m n}$

93.

$5 + 2 \sqrt{3}$

95.

$1 + 3 \sqrt{5}$

97.

$5 - 2 \sqrt{6}$

99.

$1 + \sqrt{10}$

101.

$\frac{7}{8}$

103.

$\frac{11}{4}$

105.

$\frac{6}{7}$

107.

$\frac{3}{5}$

109.

$x^{2}$

111.

$\frac{1}{y^{2}}$

113.

$10 x^{2}$

115.

$4 p^{4}$

117.

$\frac{6}{\sqrt{35}}$

119.

$\frac{2 \sqrt{5}}{9}$

121.

$\frac{4 x^{3} \sqrt{6 x}}{11}$

123.

$\frac{10 m^{2} \sqrt{3 m}}{8}$

125.

$\frac{7 r^{2} \sqrt{2 r}}{10}$

127.

$\frac{2 q^{3} \sqrt{7}}{15}$

129.

$\frac{5 r^{4} \sqrt{3 r}}{s^{4}}$

131.

$\frac{4 p^{3} \sqrt{7 p}}{q}$

133.

$\frac{5 x}{3}$

135.

$\frac{11 p \sqrt{p}}{9}$

137.

$\frac{4 x y}{3}$

139.

$\frac{1}{2 p q \sqrt{p}}$

141.

ⓐ $17.0 feet$ ⓑ $15.0 feet$

143.

Answers will vary.

Section 9.3 Exercises

145.

$3 \sqrt{2}$

147.

$9 \sqrt{5}$

149.

$− \sqrt{7}$

151.

$9 \sqrt{y}$

153.

$−3 \sqrt{a}$

155.

$7 \sqrt{c}$

157.

$6 \sqrt{b}$

159.

$5 \sqrt{m} + \sqrt{n}$

161.

$13 \sqrt{7}$

163.

$−3 \sqrt{11}$

165.

$−5 \sqrt{3} + 7 \sqrt{5}$

167.

$8 \sqrt{2} - 3 \sqrt{5}$

169.

$4 \sqrt{2 a}$

171.

$\sqrt{3 c}$

173.

$4 \sqrt{3 a b}$

175.

$\sqrt{p q}$

177.

$9 \sqrt{2}$

179.

$\sqrt{5}$

181.

$−2 \sqrt{3}$

183.

$7 \sqrt{3}$

185.

$−8 \sqrt{2}$

187.

$16 \sqrt{3}$

189.

$5 \sqrt{2}$

191.

$− \sqrt{5}$

193.

$− \sqrt{3}$

195.

$- \frac{3}{4} \sqrt{2}$

197.

$a^{2} \sqrt{2 a}$

199.

$2 c^{3} \sqrt{5 c}$

201.

$36 p^{2} \sqrt{5} - 42 p^{2} \sqrt{2}$

203.

$10 r^{4} \sqrt{2} + 12 r^{4} \sqrt{6}$

205.

$14 x \sqrt{5}$

207.

$−12 y \sqrt{2}$

209.

$3 \sqrt{8}$

211.

$−2 k^{2} \sqrt{7}$

213.

$2 \sqrt{3}$

215.

$\sqrt{2}$

217.

$\sqrt{13}$

219.

$a^{2} \sqrt{5 a}$

221.

$19 \sqrt{19}$

223.

$5 \sqrt{3}$

225.

$− \sqrt{3}$

227.

$8 x \sqrt{6}$

229.

$124.5 inches$

231.

Answers will vary.

Section 9.4 Exercises

233.

ⓐ $4$ ⓑ $18 \sqrt{6}$

235.

ⓐ $7 \sqrt{2}$ ⓑ 160

237.

$30 \sqrt{3}$

239.

$−18 \sqrt{6}$

241.

$−30 \sqrt{2}$

243.

$28 \sqrt{2}$

245.

ⓐ $5 y^{2} \sqrt{3}$ ⓑ $6 n^{2} \sqrt{n}$

247.

ⓐ $8 y^{3} \sqrt{2}$ ⓑ $11 s^{3} \sqrt{s}$

249.

$40 b^{2} \sqrt{3}$

251.

$144 d^{4}$

253.

$144 d^{4}$

255.

$−96 k^{5} \sqrt{k}$

257.

ⓐ 11 ⓑ 21

259.

ⓐ 23 ⓑ 3

261.

ⓐ −234 ⓑ 180

263.

ⓐ $105 \sqrt{2}$ ⓑ 56

265.

ⓐ $24 - 4 \sqrt{11}$ ⓑ $5 \sqrt{2} - 2 \sqrt{6}$

267.

ⓐ $−14 - 7 \sqrt{11}$ ⓑ $6 \sqrt{7} - 7 \sqrt{2}$

269.

ⓐ $44 + 8 \sqrt{11}$ ⓑ $15$

271.

ⓐ $18 - 5 \sqrt{2}$ ⓑ $\sqrt{21} - 7 \sqrt{3}$

273.

$60 + 2 \sqrt{3}$

275.

$52 + 3 \sqrt{2}$

277.

$27 - 9 \sqrt{7}$

279.

$−62 + 55 \sqrt{5}$

281.

$41 + 7 \sqrt{55}$

283.

$−81 + 44 \sqrt{78}$

285.

$18 + 7 \sqrt{w} - w$

287.

$66 + 73 \sqrt{n} + 15 n$

289.

ⓐ $27 + 8 \sqrt{11}$ ⓑ $29 - 12 \sqrt{5}$

291.

ⓐ $35 - 10 \sqrt{10}$ ⓑ $82 + 48 \sqrt{2}$

293.

97

295.

39

297.

$−127$

299.

33

301.

$−24 \sqrt{3}$

303.

$−210 \sqrt{3}$

305.

$7 y^{3} \sqrt{5}$

307.

$29$

309.

$29 - 7 \sqrt{17}$

311.

ⓐ $4.6 feet$ ⓑ $21 sq. feet$

315.

ⓐ when squaring a negative, it becomes a positive ⓑ since the negative is not included in the parenthesis, it is not squared, and remains negative

Section 9.5 Exercises

317.

$\frac{\sqrt{3}}{2}$

319.

$\frac{2 \sqrt{2}}{3}$

321.

$\frac{1 - 2 \sqrt{2}}{4}$

323.

$\frac{2 + \sqrt{5}}{2}$

325.

$\frac{4}{5}$

327.

$\frac{4}{3}$

329.

ⓐ $2 x^{2}$ ⓑ $\frac{10 m^{2}}{7}$

331.

$\frac{5 r}{6}$

333.

$\frac{3 p \sqrt{102}}{17 q^{2}}$

335.

$\frac{8 n}{3 m^{3}}$

337.

$\frac{\sqrt{2}}{2}$

339.

$\frac{1 + \sqrt{3}}{3}$

341.

$\frac{4}{5}$

343.

$y^{3} \sqrt{13}$

345.

$\frac{5 \sqrt{6}}{3}$

347.

$\frac{6 \sqrt{7}}{7}$

349.

$\frac{3 \sqrt{13}}{13}$

351.

$\frac{\sqrt{10}}{3}$

353.

$\frac{4 \sqrt{5}}{45}$

355.

$- \frac{3 \sqrt{3}}{2}$

357.

$\frac{\sqrt{15}}{10}$

359.

$\frac{\sqrt{70}}{20}$

361.

$\frac{\sqrt{133}}{35}$

363.

ⓐ $\frac{3 (3 - \sqrt{11})}{−2}$ ⓑ $−2 (1 + \sqrt{5})$

365.

ⓐ $\frac{5 (5 - \sqrt{6})}{19}$ ⓑ $3 (3 + \sqrt{7})$

367.

$\frac{\sqrt{3} (\sqrt{m} + \sqrt{5})}{m - 5}$

369.

$\frac{\sqrt{2} (\sqrt{x} + \sqrt{3})}{x - 6}$

371.

${\frac{(\sqrt{r} + \sqrt{5})}{r - 5}}^{2}$

373.

$\frac{5 y^{2}}{x}$

375.

$3 \sqrt{5}$

377.

$\frac{2 \sqrt{3}}{9}$

379.

$\frac{3 (5 - \sqrt{5})}{20}$

381.

$\frac{\sqrt{2} (\sqrt{x} + \sqrt{3})}{x - 3}$

383.

${\frac{(\sqrt{x} + 2 \sqrt{2})}{x - 8}}^{2}$

385.

$\frac{5 \sqrt{10}}{4} seconds$

387.

Answers will vary.

Section 9.6 Exercises

389.

ⓐ $yes$ ⓑ $no$

391.

ⓐ no ⓑ yes

393.

3

395.

14

397.

14

399.

$17$

401.

$\frac{13}{5}$

403.

$\frac{5}{2}$

405.

$no solution$

407.

$no solution$

409.

ⓐ $10, 11$ ⓑ $5$

411.

ⓐ $8, 9$ ⓑ $11$

413.

$3$

415.

$5$

417.

not a real number

419.

$\frac{1}{4}$

421.

ⓐ $no solution$ ⓑ $\frac{57}{16}$

423.

ⓐ $no solution$ ⓑ 6

425.

no solution

427.

36

429.

15

431.

$11.4 feet$

433.

$8 seconds$

435.

$15.8 seconds$

437.

$72 feet$

439.

$53.0 feet$

441.

Answers will vary.

Section 9.7 Exercises

443.

445.

447.

449.

451.

ⓐ $a$ ⓑ $| b |$

453.

ⓐ $| k |$ ⓑ $| p |$

455.

ⓐ $a^{2}$ ⓑ $b^{9}$

457.

ⓐ $r^{2}$ ⓑ $s^{10}$

459.

ⓐ $−2 c^{3}$ ⓑ $5 d^{5}$

461.

ⓐ $2 r^{2}$ ⓑ $3 s^{6}$

463.

ⓐ $u \sqrt[5]{u^{2}}$ ⓑ $v \sqrt[6]{v^{5}}$

465.

ⓐ $p \sqrt[5]{p^{3}}$ ⓑ $q^{2} \sqrt[3]{q^{2}}$

467.

ⓐ $5 \sqrt[3]{5}$ ⓑ $2 \sqrt[6]{2}$

469.

ⓐ $5 \sqrt[4]{5}$ ⓑ $3 \sqrt[3]{3}$

471.

ⓐ $2 a \sqrt[5]{3 a^{2}}$ ⓑ $5 b \sqrt[3]{3 b}$

473.

ⓐ $8 p \sqrt[3]{p^{2}}$ ⓑ $3 q \sqrt[4]{4 q^{3}}$

475.

ⓐ $−3 \sqrt[5]{2}$ ⓑ $not real$

477.

ⓐ $−2$ ⓑ $not real$

479.

ⓐ $d$ ⓑ $| m |$

481.

ⓐ $r^{2}$ ⓑ $| c^{3} |$

483.

ⓐ $−5$ ⓑ $4 m \sqrt[4]{m^{2}}$

485.

ⓐ $3 \sqrt[3]{6}$ ⓑ $2 | r | \sqrt[4]{2 r^{3}}$

487.

ⓐ $\frac{2 r^{2} \sqrt[5]{3 r}}{s^{3}}$ ⓑ $\frac{2 u^{3} \sqrt[6]{2 u v 3}}{v}$

489.

ⓐ $\frac{5 u^{3} \sqrt[3]{5 u}}{v}$ ⓑ $\frac{3 c^{5} \sqrt[4]{9 c}}{d^{2}}$

491.

ⓐ $2 \sqrt[3]{15 q}$ ⓑ $−4 \sqrt[4]{27}$

493.

ⓐ

ⓑ

495.

ⓐ $5 \sqrt[3]{5} - 3 \sqrt[3]{2}$ ⓑ $−2 \sqrt[4]{3}$

497.

ⓐ $3 \sqrt[4]{3} + 5 \sqrt[4]{2}$ ⓑ $13 \sqrt[3]{2}$

499.

ⓐ $2 b \sqrt[3]{10 b^{2}} + 3 b \sqrt[3]{10}$ ⓑ $2 v^{2} \sqrt[4]{10 v^{2}} - 4 \sqrt[4]{5 v^{3}}$

501.

$2$

503.

$| b |$

505.

$5 d^{5}$

507.

$s^{2} \sqrt[4]{s^{2}}$

509.

$2 y \sqrt[4]{3 y^{2}}$

511.

$not real$

513.

$2 x \sqrt[5]{2 x}$

515.

$\frac{2 u^{3} \sqrt[6]{2 u v 3}}{v}$

517.

$4 \sqrt[4]{2}$

519.

$3 u \sqrt[4]{6 u^{3}} + 4 \sqrt[4]{3 u^{3}}$

521.

$5$

523.

Answers may vary.

Section 9.8 Exercises

525.

527.

529.

531.

533.

535.

537.

ⓐ 5 ⓑ 3 ⓒ 2

539.

ⓐ 6 ⓑ 2 ⓒ 3

541.

543.

545.

547.

549.

551.

553.

555.

557.

559.

561.

563.

565.

567.

569.

571.

573.

575.

577.

579.

ⓐ $3 r^{\frac{1}{5}}$ ⓑ $2 s^{\frac{1}{14}}$

581.

ⓐ $9 m^{\frac{1}{2}}$ ⓑ $125 n^{2}$

583.

ⓐ $r^{2} s$ ⓑ $u^{3} v^{4}$

585.

ⓐ $r^{8} s^{5}$ ⓑ $u^{8} v^{4}$

587.

ⓐ $a^{3}$ ⓑ $b^{4}$

589.

ⓐ $m$ ⓑ $n^{2}$

591.

$n$

593.

$b^{6}$

595.

$\frac{1}{z^{2}}$

597.

$2 s^{\frac{1}{10}}$

599.

$u^{2} v^{3}$

601.

15.6 feet

603.

8 seconds

Review Exercises

607.

12

609.

$−9$

611.

not a real number

613.

17

615.

$12 < \sqrt{155} < 13$

617.

7.55

619.

$8 b$

621.

$15 m n$

623.

$7 y$

625.

$11 c d$

627.

$7 \sqrt{2}$

629.

$y^{9} \sqrt{y}$

631.

$6 n^{6} \sqrt{n}$

633.

$5 n^{3} \sqrt{6 n}$

635.

$6 r^{2} s \sqrt{3 r s}$

637.

$1 + \sqrt{2}$

639.

$\frac{3}{2}$

641.

$y^{2}$

643.

$6 q^{2}$

645.

$\frac{\sqrt{26}}{13}$

647.

$\frac{3 r^{2} \sqrt{r}}{2}$

649.

$\frac{2 r s^{3} \sqrt{r}}{5}$

651.

$12 \sqrt{5}$

653.

$4 \sqrt{m}$

655.

$11 \sqrt{13} + 2 \sqrt{3}$

657.

$3 \sqrt{3 r s} - 5 \sqrt{r s}$

659.

$5 \sqrt{2}$

661.

$9 \sqrt{3}$

663.

$0$

665.

$17 n^{2} \sqrt{2}$

667.

$24 \sqrt{7}$

669.

$180 y^{2}$

671.

8

673.

50

675.

$20 - 10 \sqrt{7}$

677.

$13 - 2 \sqrt{2}$

679.

$5 - 13 \sqrt{x} - 6 x$

681.

$1 + 12 \sqrt{p} + 36 p$

683.

$−19$

685.

$\frac{\sqrt{3}}{2}$

687.

$\frac{4}{3}$

689.

$y^{2} \sqrt{10}$

691.

$\frac{2 \sqrt{15}}{3}$

693.

$\frac{\sqrt{5}}{3}$

695.

$\frac{\sqrt{21}}{14}$

697.

$\frac{16 - 12 \sqrt{3}}{−11}$

699.

$−8 - 4 \sqrt{5}$

701.

$\frac{\sqrt{2 p} - \sqrt{6}}{p - 3}$

703.

5

705.

$\frac{7}{2}$

707.

no solution

709.

13

711.

$\frac{43}{2}$

713.

0

715.

$\frac{1}{16}$

717.

11

719.

7.5 seconds

721.

ⓐ 2 ⓑ 4

723.

ⓐ $d$ ⓑ $| v |$

725.

ⓐ $2 x^{2}$ ⓑ $2 y^{2}$

727.

ⓐ $d$ ⓑ

729.

ⓐ $2 c \sqrt[5]{2 c^{3}}$ ⓑ $2 d \sqrt[4]{3 d^{3}}$

731.

ⓐ $−5 \sqrt[3]{4}$ ⓑ not a real number

733.

$w^{3} \sqrt[3]{w}$

735.

$3 z^{2}$

737.

$2 \sqrt[5]{20}$

739.

$2 \sqrt[4]{2}$

741.

$2 t \sqrt[5]{3 t^{3}} + 3 \sqrt[5]{2 t^{4}}$

743.

745.

$v^{\frac{1}{6}}$

747.

${(10 z)}^{\frac{1}{6}}$

749.

2

751.

$\frac{1}{5}$

753.

$\frac{1}{6}$

755.

$n^{\frac{8}{5}}$

757.

32,768

759.

$\frac{1}{59,049}$

761.

$x^{8}$

763.

$2 s^{\frac{9}{16}}$

765.

$z^{2}$

Practice Test

767.

$13 m^{2} | n |$

769.

$4 \sqrt{13} + 5 \sqrt{2}$

771.

$180 y^{2} \sqrt{3}$

773.

$1 - 4 \sqrt{q} + 4 q$

775.

ⓐ $3 x^{3}$ ⓑ $2 y^{3}$

777.

$y \sqrt{2}$

779.

$0$

781.

343

783.

$\frac{1}{w}$

785.

$\frac{\sqrt{6}}{4}$

787.

42

789.

6.1 seconds