Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo

Be Prepared

8.1

8; −1; -729

8.2

3.85

8.3

x6x6; y6y6; z12z12

8.4

x 5 x 5

8.5

1 y 8 1 y 8

8.6

n 12 n 12

8.7

53 60 53 60

8.8

64 x 6 y 15 64 x 6 y 15

8.9

1 125 1 125

8.10

2 x 2 + 11 x 8 2 x 2 + 11 x 8

8.11

8 + 2 a a 2 8 + 2 a a 2

8.12

81 90 y + 25 y 2 81 90 y + 25 y 2

8.13

5 8 5 8

8.14

x 6 x 6

8.15

49 9 x 2 49 9 x 2

8.16

y 2 6 y + 9 y 2 6 y + 9

8.17

x = 5 2 x = 5 2

8.18

n = 2 or n = 4 n = 2 or n = 4

8.19

( , 1 2 ] ( , 1 2 ]

8.20

f ( 2 ) = 2 , f ( −1 ) = −7 , f ( 0 ) = −4 f ( 2 ) = 2 , f ( −1 ) = −7 , f ( 0 ) = −4

8.21

domain: [ 0 , ) ; range: [ 0 , ) domain: [ 0 , ) ; range: [ 0 , )

8.22

−4,0.5,73,3,81;−4,0.5,73,3,81; 7;7; −4,7,0.5,73,3,81−4,7,0.5,73,3,81

8.23

2 x 2 x 15 2 x 2 x 15

8.24

5 + 15 2 5 + 15 2

Try It

8.1

−8−8 15

8.2

10 −11−11

8.3

not a real number −9−9

8.4

−7−7 not a real number

8.5

3 4 3

8.6

10 2 4

8.7

−3−3 not real −2−2

8.8

−6−6 not real −4−4

8.9

6<38<76<38<7
4<933<54<933<5

8.10

9<84<109<84<10
5<1523<65<1523<6

8.11

3.323.32 4.144.14
3.363.36

8.12

3.613.61 4.384.38
3.153.15

8.13

|b||b| w |m||m| q

8.14

|y||y| p |z||z| q

8.15

|y9||y9| z6z6

8.16

m2m2 |b5||b5|

8.17

|u3||u3| v5v5

8.18

c4c4 d4d4

8.19

8|x|8|x| −10|p|−10|p|

8.20

13|y|13|y| −11|y|−11|y|

8.21

3x93x9 3|q7|3|q7|

8.22

5q35q3 3q53q5

8.23

10|ab|10|ab| 12p6q1012p6q10
2x10y42x10y4

8.24

15|mn|15|mn| 13|x5y7|13|x5y7|
3w12z53w12z5

8.25

4 3 4 3

8.26

3 5 3 5

8.27

122122 333333 244244

8.28

123123 553553 394394

8.29

b2bb2b |y|y24|y|y24 zz23zz23

8.30

p4pp4p yy35yy35
q2q6q2q6

8.31

4y22y4y22y 3p32p33p32p3
2q24q242q24q24

8.32

5a43a5a43a 4m32m234m32m23
3|n|2n343|n|2n34

8.33

7|a3|b22ab7|a3|b22ab
2xy7x2y32xy7x2y3 2|x|y22x42|x|y22x4

8.34

6m4|n5|5mn6m4|n5|5mn
2x2y9y232x2y9y23 2|xy|5x342|xy|5x34

8.35

−4−4 no real numberno real number

8.36

−553−553 no real number

8.37

5+535+53 2323

8.38

2+722+72 2525

8.39

5454 3535 2323

8.40

7979 2525 1313

8.41

|a||a| |x||x| y3y3

8.42

x2x2 m2m2 n2n2

8.43

2 | p | 6 p 7 2 | p | 6 p 7

8.44

2 x 2 3 x 5 2 x 2 3 x 5

8.45

4|m|5m|n3|4|m|5m|n3| 3c34c3d23c34c3d2
2x25x24|y|2x25x24|y|

8.46

3u36uv43u36uv4 2r53s22r53s2
3|m3|2m24|n3|3|m3|2m24|n3|

8.47

5|y|x65|y|x6 2xyy2332xyy233
|ab|a42|ab|a42

8.48

2|m|35|n3|2|m|35|n3| 3xyx2353xyx235
2|ab|a2432|ab|a243

8.49

7z27z2 −523−523
3|m|2m243|m|2m24

8.50

8m48m4 −4−4 3|n|243|n|24

8.51

tt m3m3 r4r4

8.52

b6b6 z5z5 p4p4

8.53

(10m)12(10m)12 (3n)15(3n)15
3(6y)143(6y)14

8.54

(3k)17(3k)17 (5j)14(5j)14
8(2a)138(2a)13

8.55

6 2 2

8.56

10 3 3

8.57

No real solution −8−8
1818

8.58

No real solution −4−4
1414

8.59

x52x52 (3y)34(3y)34 (2m3n)52(2m3n)52

8.60

a25a25 (5ab)53(5ab)53
(7xyz)32(7xyz)32

8.61

9 17291729 1818

8.62

8 1919 11251125

8.63

−64−64 164164 not a real number

8.64

−729−729 17291729 not a real number

8.65

x32x32 x8x8 1x1x

8.66

y118y118 m2m2 1d1d

8.67

8x158x15 x12y13x12y13

8.68

729n35729n35 a2b23a2b23

8.69

m2m2 5nm145nm14

8.70

u3u3 3x15y133x15y13

8.71

22 11x311x3
3x45y43x45y4

8.72

−43−43 8y38y3
5m42m35m42m3

8.73

−27x−27x 5xy45xy4

8.74

3y3y 37mn337mn3

8.75

9292 223223 3333

8.76

7373 −1053−1053 −323−323

8.77

m32mm32m x25x3x25x3

8.78

p3pp3p
4y4y232y4n234y4y232y4n23

8.79

12151215 −1843−1843

8.80

272272 −3623−3623

8.81

288x35288x35 8y6y248y6y24

8.82

144y25y144y25y −36a3a4−36a3a4

8.83

18+618+6 −243233−243233

8.84

−40+42−40+42 −3183−3183

8.85

−66+157−66+157
x235x3+6x235x3+6

8.86

411411411411
x23+4x3+3x23+4x3+3

8.87

1 + 9 21 1 + 9 21

8.88

−12 20 3 −12 20 3

8.89

102+202102+202 55+6655+66

8.90

4112541125
12136101213610

8.91

−11 −11

8.92

−159 −159

8.93

5s85s8 2a2a

8.94

5q265q26 2b2b

8.95

9x2y29x2y2 −4xy−4xy

8.96

10n3m10n3m −3pq2−3pq2

8.97

4 x y 2 x 4 x y 2 x

8.98

4 a b 3 b 4 a b 3 b

8.99

533533 6868 2xx2xx

8.100

655655 146146 5xx5xx

8.101

49374937 90369036 53y233y53y233y

8.102

432432 150310150310 25n235n25n235n

8.103

27432743 12441244 35x345x35x345x

8.104

1254512545 14441444
24x34x24x34x

8.105

3 ( 1 + 5 ) 4 3 ( 1 + 5 ) 4

8.106

4 + 6 5 4 + 6 5

8.107

5 ( x 2 ) x 2 5 ( x 2 ) x 2

8.108

10 ( y + 3 ) y 3 10 ( y + 3 ) y 3

8.109

( p + 2 ) p 2 2 ( p + 2 ) p 2 2

8.110

( q 10 ) q 10 2 ( q 10 ) q 10 2

8.111

m = 23 3 m = 23 3

8.112

z = 3 10 z = 3 10

8.113

no solution no solution

8.114

no solution no solution

8.115

x = 2 , x = 3 x = 2 , x = 3

8.116

y = 5 , y = 6 y = 5 , y = 6

8.117

x = −6 x = −6

8.118

x = −9 x = −9

8.119

x = 8 x = 8

8.120

x = 6 x = 6

8.121

m = 7 m = 7

8.122

n = 3 n = 3

8.123

a = 63 a = 63

8.124

b = 311 b = 311

8.125

x = 3 x = 3

8.126

x = 6 5 x = 6 5

8.127

x = 4 x = 4

8.128

x = 9 x = 9

8.129

x = 5 x = 5

8.130

x = 0 x = 4 x = 0 x = 4

8.131

9 seconds

8.132

3.53.5 seconds

8.133

42.742.7 feet

8.134

54.154.1 feet

8.135

f(6)=4f(6)=4 no value at x=0x=0

8.136

g(4)=5g(4)=5 no value at f(−3)f(−3)

8.137

g(4)=2g(4)=2 g(1)=−1g(1)=−1

8.138

h(2)=2h(2)=2
h(−5)=−3h(−5)=−3

8.139

f(4)=2f(4)=2 f(−1)=1f(−1)=1

8.140

g(16)=3g(16)=3 g(3)=2g(3)=2

8.141

[ 5 6 , ) [ 5 6 , )

8.142

( , 4 5 ] ( , 4 5 ]

8.143

( −3 , ) ( −3 , )

8.144

( 5 , ) ( 5 , )

8.145

( , ) ( , )

8.146

( , ) ( , )

8.147

domain: [−2,)[−2,)

The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 2 to 6. The y-axis runs from 0 to 8. The function has a starting point at (negative 2, 0) and goes through the points (negative 1, 1) and (2, 2).


range: [0,)[0,)

8.148

domain: [2,)[2,)

The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 6. The function has a starting point at (2, 0) and goes through the points (3, 1) and (6, 2).


range: [0,)[0,)

8.149

domain: (,)(,)

The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 2 to 2. The y-axis runs from negative 2 to 2. The function has a center point at (0, 0) and goes through the points (1, negative 1) and (negative 1, 1).


range: (,)(,)

8.150

domain: (,)(,)

The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 1 to 5. The y-axis runs from negative 3 to 3. The function has a center point at (2, 0) and goes through the points (1, negative 1) and (3, 2).


range: (,)(,)

8.151

9i9i 5i5i 32i32i

8.152

6i6i 3i3i 33i33i

8.153

6 2 i 6 2 i

8.154

7 3 i 7 3 i

8.155

6+5i6+5i 63i63i

8.156

−26i−26i 2+9i2+9i

8.157

12 + 20 i 12 + 20 i

8.158

12 6 i 12 6 i

8.159

−11 7 i −11 7 i

8.160

−5 10 i −5 10 i

8.161

−21 + 21 i −21 + 21 i

8.162

9 40 i 9 40 i

8.163

−14 −14

8.164

−54 −54

8.165

−12 22 3 i −12 22 3 i

8.166

6 + 12 2 i 6 + 12 2 i

8.167

25

8.168

29

8.169

109

8.170

41

8.173

4 17 + 16 17 i 4 17 + 16 17 i

8.174

2 5 + 4 5 i 2 5 + 4 5 i

8.175

3 2 3 2 i 3 2 3 2 i

8.176

4 5 2 5 i 4 5 2 5 i

8.177

i i

8.178

1 1

Section 8.1 Exercises

1.

8 −9−9

3.

14 −1−1

5.

2323 −0.1−0.1

7.

not real number −17−17

9.

−15−15 not real number

11.

6 4

13.

8 3 1

15.

−2−2 not realnot real −2−2

17.

−5−5 not realnot real −4−4

19.

8<70<98<70<9
4<713<54<713<5

21.

14<200<1514<200<15
5<1373<65<1373<6

23.

4.364.36 4.464.46
3.143.14

25.

7.287.28 5.285.28
4.614.61

27.

u |v||v|

29.

|y||y| mm

31.

|x3||x3| y8y8

33.

x12x12 |y11||y11|

35.

x3x3 |y3||y3|

37.

m2m2 n4n4

39.

7|x|7|x| −9|x9|−9|x9|

41.

11m1011m10 −8|a|−8|a|

43.

2x22x2 2y22y2

45.

6a26a2 2b42b4

47.

12|xy|12|xy| 13w4|y5|13w4|y5|
2a17b22a17b2

49.

11|ab|11|ab| 3c4d63c4d6
4x5y224x5y22

51.

Answers will vary.

53.

Answers will vary.

Section 8.2 Exercises

55.

3 3 3 3

57.

5 5 5 5

59.

7 3 7 3

61.

20 2 20 2

63.

224224 225225

65.

244244 443443

67.

| y5 |y| y5 |y rr23rr23 s2s24s2s24

69.

n10nn10n q2q23q2q23
|n|n28|n|n28

71.

5r65r5r65r 3x4x233x4x23
2|y|3y242|y|3y24

73.

11|m11|2m11|m11|2m 3m25m243m25m24 2n5n352n5n35

75.

7|m3n5|3mn7|m3n5|3mn 2x2y26y32x2y26y3 2|xy|2x42|xy|2x4

77.

8|qr3|3qr8|qr3|3qr 3m3n32n33m3n32n3 3a2b2a43a2b2a4

79.

−643−643 not real

81.

−2−2 not real

83.

5+235+23 5656

85.

1+351+35 1+101+10

87.

3434 2323 1313

89.

5353 3535 1414

91.

x2x2 p3p3 |q||q|

93.

1y21y2 u2u2 |v3||v3|

95.

4 | x 3 | 6 x 11 4 | x 3 | 6 x 11

97.

5 m 2 3 m 4 5 m 2 3 m 4

99.

7 r 2 2 r 10 7 r 2 2 r 10

101.

2 | q 3 | 7 15 2 | q 3 | 7 15

103.

5r43rs45r43rs4 3a22a23b3a22a23b
2|c|4c4|d|2|c|4c4|d|

105.

2|p3|7p|q|2|p3|7p|q| 3s23s23t3s23s23t
2|p3|4p34|q3|2|p3|4p34|q3|

107.

4|xy|34|xy|3 y2x32y2x32 |ab|a42|ab|a42

109.

12|pq|12|pq| 2cdd2352cdd235
|mn|2|mn|2

111.

3p4p|q|3p4p|q| 224224
2x2x52x2x5

113.

5|m3|5|m3| 553553
3|y|3y243|y|3y24

115.

Answers will vary.

117.

Answers will vary.

Section 8.3 Exercises

119.

xx y3y3 z4z4

121.

u5u5 v9v9 w20w20

123.

x17x17 y19y19 f15f15

125.

(7c)13(7c)13 (12d)17(12d)17
2(6b)142(6b)14

127.

(21p)12(21p)12 (8q)14(8q)14
4(36r)164(36r)16

129.

9 5 8

131.

2 4 5

133.

−6−6 −6−6 1616

135.

not real −3−3 1313

137.

not real −6−6 1616

139.

not real −10−10 110110

141.

m52m52 (3y)73(3y)73 (4x5y)35(4x5y)35

143.

u25u25 (6x)53(6x)53 (18a5b)74(18a5b)74

145.

32,768 17291729 9

147.

4 1919 not real

149.

−27−27 127127 not real

151.

c78c78 p9p9 1r1r

153.

y54y54 x8x8 1m1m

155.

81q281q2 a12ba12b

157.

8u148u14 8p12q348p12q34

159.

r72r72 6st6st

161.

c2c2 2x3y2x3y

163.

Answers will vary.

Section 8.4 Exercises

165.

3232 7m37m3 6m46m4

167.

9595 12a312a3 62z462z4

169.

42a42a 0

171.

3c3c 4pq34pq3

173.

−23−23 −253−253 324324

175.

7373 723723 354354

177.

a22aa22a 0

179.

2c35c2c35c 14r22r2414r22r24

181.

4 y 2 4 y 2

183.

−186−186 −6493−6493

185.

−302−302 624624

187.

72z2372z23 45x22345x223

189.

−42z52z−42z52z −8y6y4−8y6y4

191.

14+5714+57 463+343463+343

193.

4431144311 324+544324+544

195.

60 + 2 3 60 + 2 3

197.

30+18230+182 x232x33x232x33

199.

−55+1310−55+1310
2x23+8x3+62x23+8x3+6

201.

23 + 3 30 23 + 3 30

203.

−439 2 77 −439 2 77

205.

14+6514+65 7920379203

207.

8718687186
163+607163+607

209.

14

211.

−227 −227

213.

19 19

215.

9 x 2 3 4 9 x 2 3 4

217.

5 3 5 3

219.

9 2 9 2

221.

5 4 5 4

223.

10c239c33 10 c 2 3 9 c 3 3

225.

2 3 2 3

227.

17 q 2 17 q 2

229.

3 7 3 7

231.

−42 9 3 −42 9 3

233.

29

235.

29 7 17 29 7 17

237.

54 36 2 54 36 2

239.

6 + 3 2 3 6 + 3 2 3

241.

Answers will vary.

243.

Answers will vary.

Section 8.5 Exercises

245.

4343 4343

247.

10m2710m27 3y3y

249.

56r256r2 2x32x3

251.

6pq26pq2 2a2b2a2b

253.

8m43n48m43n4 2x23y22x23y2

255.

2 x 2 7 y 2 x 2 7 y

257.

2 a b 2 a 3 2 a b 2 a 3

259.

563563 239239 25xx25xx

261.

677677 2101521015 43pp43pp

263.

25352535 45364536 26a233a26a233a

265.

121311121311 28362836 9x3x9x3x

267.

3434734347 40444044 24x24x24x24x

269.

943943 50445044 23a34a23a34a

271.

−2 ( 1 + 5 ) −2 ( 1 + 5 )

273.

3 ( 3 + 7 ) 3 ( 3 + 7 )

275.

3 ( m + 5 ) m 5 3 ( m + 5 ) m 5

277.

2 ( x + 6 ) x 6 2 ( x + 6 ) x 6

279.

( r + 5 ) r 5 2 ( r + 5 ) r 5 2

281.

( x + 2 2 ) x 8 2 ( x + 2 2 ) x 8 2

283.

Answers will vary.

285.

Answers will vary.

Section 8.6 Exercises

287.

x = 14 x = 14

289.

no solution

291.

x = −4 x = −4

293.

m = 14 m = 14

295.

v = 17 v = 17

297.

m = 7 2 m = 7 2

299.

no solution

301.

u = 3 , u = 4 u = 3 , u = 4

303.

r = 1 , r = 2 r = 1 , r = 2

305.

x = 10 x = 10

307.

x = −8 x = −8

309.

x = 8 x = 8

311.

x = −4 x = −4

313.

x = 7 x = 7

315.

x = 3 x = 3

317.

z = 21 z = 21

319.

x = 42 x = 42

321.

r = 3 r = 3

323.

u = 3 u = 3

325.

r = −2 r = −2

327.

x = 1 x = 1

329.

x = −8 , x = 2 x = −8 , x = 2

331.

a = 0 a = 0

333.

u = 9 4 u = 9 4

335.

a = 4 a = 4

337.

x = 0 x = 4 x = 0 x = 4

339.

x = 1 x = 5 x = 1 x = 5

341.

x = 9 x = 9

343.

8.78.7 feet

345.

4.74.7 seconds

347.

72 feet

349.

Answers will vary.

Section 8.7 Exercises

351.

f(5)=4f(5)=4 no value at x=0x=0

353.

g(4)=5g(4)=5 g(8)=7g(8)=7

355.

F(1)=1F(1)=1 F(−11)=5F(−11)=5

357.

G(5)=26G(5)=26 G(2)=3G(2)=3

359.

g(6)=2g(6)=2 g(−2)=−2g(−2)=−2

361.

h(−2)=0h(−2)=0 h(6)=243h(6)=243

363.

f(0)=0f(0)=0 f(2)=2f(2)=2

365.

g(1)=0g(1)=0 g(−3)=2g(−3)=2

367.

[ 1 3 , ) [ 1 3 , )

369.

( , 2 3 ] ( , 2 3 ]

371.

( 2 , ) ( 2 , )

373.

( , −3 ] ( 2 , ) ( , −3 ] ( 2 , )

375.

( , ) ( , )

377.

( , ) ( , )

379.

[ 3 8 , ) [ 3 8 , )

381.

( , ) ( , )

383.

domain: [−1,)[−1,)

The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 1 to 7. The y-axis runs from negative 2 to 10. The function has a starting point at (negative 1, 0) and goes through the points (0, 1) and (3, 2).


[0,)[0,)

385.

domain: [−4,)[−4,)

The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The function has a starting point at (negative 4, 0) and goes through the points (negative 3, 1) and (0, 2).


[0,)[0,)

387.

domain: [0,)[0,)

The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 8. The function has a starting point at (0, 2) and goes through the points (1, 3) and (4, 4).


[2,)[2,)

389.

domain: [0,)[0,)

The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 8. The function has a starting point at (0, 0) and goes through the points (1, 2) and (4, 4).


[0,)[0,)

391.

domain: (,3](,3]

The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 6 to 4. The y-axis runs from 0 to 8. The function has a starting point at (3, 0) and goes through the points (2, 1), (negative 1, 2), and (negative 6, 3).


[0,)[0,)

393.

domain: [0,)[0,)

The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from negative 8 to 0. The function has a starting point at (0, 0) and goes through the points (1, negative 1) and (4, negative 2).


(,0](,0]

395.

domain: (,)(,)

The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (negative 1, 0) and goes through the points (negative 2, negative 1) and (0, 1).


(,)(,)

397.

domain: (,)(,)

The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (negative 4, 0) and goes through the points (negative 3, negative 1) and (negative 1, 1).


(,)(,)

399.

domain: (,)(,)

The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The function has a center point at (0, 3) and goes through the points (negative 1, 2) and (1, 4).


(,)(,)

401.

domain: (,)(,)

The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (0, 0) and goes through the points (1, 1) and (negative 1, negative 1).


(,)(,)

403.

domain: (,)(,)

The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (0, 0) and goes through the points (1, 2) and (negative 1, negative 2).


(,)(,)

405.

Answers will vary.

407.

Answers will vary.

Section 8.8 Exercises

409.

4i4i 11i11i 22i22i

411.

10i10i 13i13i 35i35i

413.

9 3 i 9 3 i

415.

8 2 i 8 2 i

417.

8 + 7 i 8 + 7 i

419.

14 + 2 i 14 + 2 i

421.

−2 + 2 i −2 + 2 i

423.

8 + 5 i 8 + 5 i

425.

7 13 i 7 13 i

427.

25 2 2 i 25 2 2 i

429.

12 + 20 i 12 + 20 i

431.

−12 + 18 i −12 + 18 i

433.

−38 + + 9 i −38 + + 9 i

435.

27 + 15 i 27 + 15 i

437.

−7 + 24 i −7 + 24 i

439.

−5 + 12 i −5 + 12 i

441.

−30 −30

443.

−30 −30

445.

−44 4 i 3 −44 4 i 3

447.

−20 2 2 i −20 2 2 i

449.

5

451.

53

453.

50

455.

85

457.

i

459.

2 25 + 11 25 i 2 25 + 11 25 i

461.

6 13 + 9 13 i 6 13 + 9 13 i

463.

12 13 8 13 i 12 13 8 13 i

465.

4 3 1 3 i 4 3 1 3 i

467.

3 4 + 1 2 i 3 4 + 1 2 i

469.

i

471.

−1 −1

473.

1

475.

i

477.

Answers will vary.

479.

Answers will vary.

Review Exercises

481.

15 −4−4

483.

2 3 3

485.

8<68<98<68<9
4<843<54<843<5

487.

a bb

489.

m2m2 n4n4

491.

6a26a2 2b42b4

493.

5 5 5 5

495.

553553 226226

497.

4|s7|5s4|s7|5s 2a3a252a3a25
2|b|2b62|b|2b6

499.

−2−2 not real

501.

6767 2323 1212

503.

5 m 2 3 m 4 5 m 2 3 m 4

505.

12|pq|12|pq| 2cd5d232cd5d23
|mn|2|mn|2

507.

rr s3s3 t4t4

509.

5 3 2

511.

−2−2 1313 −5−5

513.

125 127127 16

515.

6363 b9b9 1w1w

517.

4242 9p39p3 2x32x3

519.

7373 723723 354354

521.

37 y 3 37 y 3

523.

126x2x126x2x 48a5a2348a5a23

525.

7122771227
x238x3+15x238x3+15

527.

27+81127+811 2912529125

529.

9 x 2 3 4 9 x 2 3 4

531.

8m43n48m43n4 2x23y22x23y2

533.

121311121311 28362836 9x3x9x3x

535.

7 ( 2 + 6 ) 2 7 ( 2 + 6 ) 2

537.

( x + 2 2 ) x 8 2 ( x + 2 2 ) x 8 2

539.

no solution

541.

u = 3 , u = 4 u = 3 , u = 4

543.

x = −4 x = −4

545.

r = 3 r = 3

547.

x = −8 , x = 2 x = −8 , x = 2

549.

x = 3 x = 3

551.

64.864.8 feet

553.

G(5)=26G(5)=26 G(2)=3G(2)=3

555.

g(1)=0g(1)=0 g(−3)=2g(−3)=2

557.

( 2 , ) ( 2 , )

559.

, 10 7 , 10 7

561.

domain: [0,)[0,)

The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 8. The function has a starting point at (0, 0) and goes through the points (1, 2) and (4, 4).


range: [0,)[0,)

563.

domain: (,)(,)

The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The function has a center point at (0, 3) and goes through the points (negative 1, 2) and (1, 4).


range: (,)(,)

565.

8 2 i 8 2 i

567.

8 + 5 i 8 + 5 i

569.

23 + 14 i 23 + 14 i

571.

−8 −8

573.

−5 + 12 i −5 + 12 i

575.

2 25 + 11 25 i 2 25 + 11 25 i

577.

1

Practice Test

579.

5 x 3 5 x 3

581.

2 x 2 y 9 x 2 y 3 2 x 2 y 9 x 2 y 3

583.

1414 −343−343

585.

x 7 4 x 7 4

587.

x 2 3 x x 2 3 x

589.

36 x 4 2 36 x 4 2

591.

2 7 3 2 7 3

593.

7 x 2 x 3 | y 3 | y 7 x 2 x 3 | y 3 | y

595.

3 ( 2 3 ) 3 ( 2 3 )

597.

−12 + 8 i −12 + 8 i

599.

1 1

601.

x = 4 x = 4

603.

domain: [−2,)[−2,)

The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 2 to 6. The y-axis runs from 0 to 8. The function has a starting point at (negative 2, 0) and goes through the points (negative 1, 1) and (2, 2).


range: [0,)[0,)

Order a print copy

As an Amazon Associate we earn from qualifying purchases.

Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
    Access for free at https://openstax.org/books/intermediate-algebra-2e/pages/1-introduction
  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
    Access for free at https://openstax.org/books/intermediate-algebra-2e/pages/1-introduction
Citation information

© Jan 23, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.