Intermediate Algebra (11th edition)

99. 
    
    
    
    101. 
         
         
         
         103. 
              
              
              
              105. 
                   
              
              
              
              
         
         
         
         
    
    
    
    


100. 
     
     
     
     109. 111.Each expression is approximately
     
     
     
     

equal to 0.2588190451. 113. 115.

117. 
     
     
     
     119. 
          
     
     
     
     

Summary Exercises on Operations with Radicals and

Rational Exponents (pages 466 – 467)

1. 
   
   
   
   2. 
      
      
      
      3. 
         
         
         
         4. 
            
         
         
         
         
      
      
      
      
   
   
   
   


2. 
   
   
   
   6. 
      
      
      
      7. 
         
         
         
         8. 
            
         
         
         
         
      
      
      
      
   
   
   
   


3. 
   
   
   
   10. 
       
       
       
       11. 
           
           
           
           12. 
               
           
           
           
           
       
       
       
       
   
   
   
   


4. 
   
   
   
   14. 
       
       
       
       15. 
           
           
           
           16. 
               
               
               
               17. 
                   
               
               
               
               
           
           
           
           
       
       
       
       
   
   
   
   


5. 
   
   
   
   19. 
       
       
       
       20. 
           
           
           
           21. 
               
           
           
           
           
       
       
       
       
   
   
   
   


6. 
   
   
   
   23. 
       
       
       
       24. 
           
       
       
       
       
   
   
   
   


7. 
   
   
   
   26. 
       
       
       
       27. 
           
           
           
           28. 
               
               
               
               29. 
                   
               
               
               
               
           
           
           
           
       
       
       
       
   
   
   
   


8. or 31. 32.


9. (a) 8 (b) 34. (a) 10 (b)


10. (a) (b) 36. (a) (b)


11. (a) (b) 38. (a) (b)


12. (a) (b)0.2 40. (a) (b)0.3

Section 8.6 (pages 472– 474)

1. (a)yes (b)no 3. (a)yes (b)no 5.No. There is no solution.

The radical expression, which is positive, cannot equal a negative number.

7. 
   
   
   
   9. 
      
      
      
      11. 
          
          
          
          13. 
              
              
              
              15. 
                  
                  
                  
                  17. 
                      
                      
                      
                      19. 
                          
                      
                      
                      
                      
                  
                  
                  
                  
              
              
              
              
          
          
          
          
      
      
      
      
   
   
   
   


8. 
   
   
   
   23. 
       
       
       
       25. 
           
           
           
           27. 
               
               
               
               29. 
                   
                   
                   
                   31. 
                       
                       
                       
                       33. 35.It is incorrect to just square each term. The right side should be
                       
                       
                       
                       
                   
                   
                   
                   
               
               
               
               
           
           
           
           
       
       
       
       
   
   
   
   

The correct first step is

and the solution set is 37. 39.

41. 
    
    
    
    43. 
        
        
        
        45. 
            
            
            
            47. 
                
                
                
                49. 
                    
                    
                    
                    51. 
                        
                    
                    
                    
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


42. 
    
    
    
    55. 
        
        
        
        57. 
            
            
            
            59. 
                
                
                
                61. 
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


43. 
    
    
    
    65. 
        
        
        
        67. 
            
            
            
            69. 
                
            
            
            
            
        
        
        
        
    
    
    
    


44. 
    
    
    
    73. 
        
        
        
        75. 
            
        
        
        
        
    
    
    
    

Section 8.7 (pages 479– 481)

1.i 3. 5. 7. 13 i 9. 11. 13.

15. 
    
    
    
    17. 
        
        
        
        19. 
            
            
            
            21. 
                
                
                
                23. 5 i 25.
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    

27.Any real number acan be written as a complex number with
imaginary part 0. 29.- 1 + 7 i 31. 0 33. 7 + 3 i 35.- 2

a+ 0 i,

• 
  

  2105 - 10 i 233 23 - 2

  
  
  
  
  • 1 - i - 12 i i 25 4 i 23
  
  
  
  


• 
  

  (^7) A 5 + (^22) B
  23
  1 +x 2 x^2 +x- 15
  r=
  a
  4 p^2 N^2
  M=
  r^2 F
  m
  K=
  V^2 m
  2
  L=CZ^2
  5 4, 20 6 0 E 45 F 5 9, 17 6 E^14 , 1F
  5146 586 506 0 576 576
  64 - 16 x+x^2 , 546. 516 5 - 16
  18 - x 22 = 64 - 16 x+x^2. 3 x+ 4 =
  5176 556 0 506 506 0 516
  (^5116) E 31 F 0 556 5186 556 546
  5 - 0.2, 0.2 6 5 - 0.3, 0.3 6

  
  


• 
  

  119 E- 119 , 119 F - 107 E- 107 , 107 F

  
  

5 - 4, 4 6 - 4 5 - 5, 5 6 - 5

5 - 8, 8 6 5 - 10, 10 6

7 + 4 # 3 1/2, 7 + 423 3232 x^2 - 2

1

25 x^2

• 423 - 3 xy6/5 x^10 y
  x 23 x^2
  y

1 + 233 + 239

322 + 215 + 242 + (^23522427) - 2
23117
9
11 + 2230 - 323 x 52 - 3023

• 23100
  22
  8

8

5

215 x

5 x

3 A 25 - 2 B

2 abc^323 b^25233

2 x+ 25

x- 5

• 44

4 A 27 - 25 B - 3 + 222

• 26
  2
  73 + 12235


• 6210 7 - 214 2 + 26 - 223 - 322 422

E^38 F E- 31 , 23 F

4 x-y

3 xA 22 x + 2 y B

33

8 A 6 + 23 B

p 2 p+ 2

p+ 2

32 x+y

x+y

6 + 226 p

3

4 - 222

3

3 - 226 1 - 25

37. 
    
    
    
    39. 
        
        
        
        41. 
            
            
            
            43. 
                
                
                
                45. 
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


38. 
    
    
    
    49. 
        
        
        
        51. 
            
            
            
            53. 
                
            
            
            
            
        
        
        
        
    
    
    
    


39. 153 57. 97 59. 4 61. 63. 65.


40. 
    
    
    
    69. 
        
        
        
        71. 
            
            
            
            73. 
                
                
                
                75. 77.i 79. 81. 83. 85.Since
                    the student multiplied by 1, which is justified by the identity property for
                    multiplication. 87. 89.Substitute both and
                    for x, and show that the result is in each case. 91.
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


41. 
    
    
    
    95. 
        
        
        
        97. 
            
            
            
            99. 
                
            
            
            
            
        
        
        
        
    
    
    
    

Chapter 8 Review Exercises (pages 487– 490)

1. 42 2. 3. 6 4. 5. 6. 7. is not a real
   number if nis even and ais negative. 8.(a) (b) (c)x


2. 
   
   
   
   10. 11.4.960 12.0.009 13.
       14.-0.189
   
   
   
   
   
   
   • 6.856 -5.053 -3968.503
   
   
   
   

|x| -|x|

• 
  

  17 - 5 - 3 - 2 2 na

  
  


• 
  

  1013 + 1011 i E-^136 F 5 - 8, 5 (^6) E- 52 , 1F
  37
  10 -
  19
  0 = 0 10 i
  (^12) + 21 i 1 + 5 i 1 - 5 i

  
  


• 
  

  1 - i -i i^20 = 1 i^425 = 15 =1,

  
  


• 
  

  1 + 2 i - 135 - 1312 i 1 - 3 i 1 + 3 i - 1

  
  

a-bi 1 +i 2 + 2 i

• 10 - 30 i 10 - 5 i - 9 + 40 i - 16 + 30 i

1 + 13 i 6 + 6 i 4 + 2 i - 81 - 16

Answers to Selected Exercises A-19

15.

domain: ;

range:

16.

domain: ;

range: 1 - q, q 2

1 - q, q 2

x

y

–1 1 8

2

6

–8

f(x) =^3 √x + 4

3 0, q 2

3 1, q 2

x

y

01 5

2

f(x) = √x – 1

17.B 18.cube (third); 8; 2; second; 4; 4 19.A 20. (a)mmust be

even. (b)mmust be odd. 21.no 22. 7 23. 24. 32

25. 
    
    
    
    26. 
        
        
        
        27. 
            
            
            
            28. 29.It is not a real number.
            
            
            
            
        
        
        
        
    
    
    
    


26. ; 31.The radical is equivalent to
    For example, and


27. 
    
    
    
    33. or 34.
    
    
    
    


28. 
    
    
    
    36. 
        
        
        
        37. 96 38. 39. 40.
        
        
        
        
    
    
    
    


29. 
    
    
    
    42. 
        
        
        
        43. 
            
            
            
            44. 
                
                
                
                45. 
                    
                    
                    
                    46. 
                        
                    
                    
                    
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


30. 
    
    
    
    48. 
        
        
        
        49. 
            
            
            
            50. 51.The product rule for ex-
                ponents applies only if the bases are the same. 52. 53.
            
            
            
            
        
        
        
        
    
    
    
    


31. 
    
    
    
    55. 
        
        
        
        56. 
            
            
            
            57. 
                
                
                
                58. 
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


32. 
    
    
    
    60. 
        
        
        
        61. 
            
            
            
            62. 
                
            
            
            
            
        
        
        
        
    
    
    
    


33. 
    
    
    
    64. 
        
        
        
        65. 
            
            
            
            66. 
                
                
                
                67. 
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


34. 
    
    
    
    69. 
        
        
        
        70. 
            
            
            
            71. 
                
                
                
                72. 10 73.
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


35. 
    
    
    
    75. 
        
        
        
        76. 
            
            
            
            77. 
                
                
                
                78. 
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


36. 
    
    
    
    80. 
        
        
        
        81. 
            
        
        
        
        
    
    
    
    


37. 
    
    
    
    83. 2 84. 85. 86. 29
    
    
    
    


38. 
    
    
    
    88. 89.The denominator would become which is not rational.
    
    
    
    


39. 
    
    
    
    91. 
        
        
        
        92. 
            
            
            
            93. 
                
                
                
                94. 
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


40. 
    
    
    
    96. 
        
        
        
        97. 
            
            
            
            98. 
                
            
            
            
            
        
        
        
        
    
    
    
    


41. 
    
    
    
    100. 
         
         
         
         101. 526 102. 566 103. 0
         
         
         
         
    
    
    
    
    
    
    • 6 + 23
      2
    
    
    
    

1 - 422

3

1 - 25

4

(^5) A 26 + (^3) B
3
22 - 27

• 5

3 m 234 n

n^2

• 2345
  5

222

4

327 py

y

• 326
  230
  5

2362 = 2336 ,

2232 y^2 + 2234 y- 3 4.801960973Z66.28725368

1 - 23 9 - 722 15 - 2226

• 8242 A 1622 + 2423 B ft A 1223 + 522 B ft


• 1122 2325 723 y 26 m 26 m 19232

215 p 2 p 2122000 210 x^72197

a^224 a

3

23 r^2

2

m^5

3

y 2 y

12

2 r^2 t 2379 r^2 t

• 3234 10 y^32 y 4 pq^223 p 3 a^2 b 234 a^2 b^2

2330 2421 225 523 - 525

266 25 r

z1/12 x1/8 x1/15 x1/36

r1/2+r s1/2 r3/2 p1/2 k9/4 m13/3

z1/2x8/5

4

1

y1/2

p4/5 52 , or 25 a2/3

7 9/2

1

2313 a+b 25

1

A^233 a+bB

5

2 m+ 3 n^ ,

2382 = 2364 =4, 8 2/3= 18 1/3 22 = 22 =4.

A 238 B 2382 2 nam am/n.

2

1000

• 
  
  
  
  • (^3227)
    216
  
  
  
  


• 
  

  (^4125)

  
  


• 
  

  11