Beginning Algebra, 11th Edition

[4.1–4.3]9. 10. [5.1, 5.2]11. 12.

[5.4]13. [5.6]14.

[5.5]15. [5.7]16.

[6.3]17. 18.prime
[6.4]19. [6.5]20.

21. [6.6]22. or 23.6 m [7.1]24.A 25.D

[7.4]26. 27. 28. 29.

[7.2]30. [7.5]31. [7.6]32. 33.

[7.7]34. hr [7.8]35.32.97 in.

ROOTS AND RADICALS

Connections ( page 498) 1. , or.

2. 3.Subtract 2abfrom each side to get.

Section 8.1 (pages 500–504)

1.true 3.false; Zero has only one square root. 5.true 7.

9. , 8 11. , 13 13. , 15. , 30 17. 1 19. 7


10. 
    
    
    
    23. 25.0.8 27.It is not a real number. 29.It is not
        a real number. 31. 19 33. 19 35. 37. 39.amust be
        positive. 41.amust be negative. 43.rational; 5 45.irrational;
        5.385 47.rational; 49.irrational; 51.It is not a real
        number. 53.irrational; 34.641 55.9 and 10 57.7 and 8
    
    
    
    


11. and 61.4 and 5 63.C 65. 67.


12. 71.24 cm 73.80 ft 75.195 ft 77.11.1 ft
    79.158.6 ft 81.9.434 83.The area of the square on the left is
    The small square inside that figure has area
    The sum of the areas of the two rectangles in the figure on the right is
    2 ab. Since the areas of the two figures are the same, we have
    which simplifies to 85. 5


13. 13 89. 91. 93.1; 8; 27; 64; 125; 216; 343; 512;
    729; 1000 95. 1 97. 5 99. 101. 103. 2 105. 5


14. 6 109.It is not a real number. 111. 113. 115.2.289
    117.5.074 119. 121. 123. 125.23 is a
    prime number.

Section 8.2 (pages 510–512)

1. 
   
   
   
   3. 
      
      
      
      5. 
         
         
         
         7. or 9 9. 13 11.
            13.A 15. 17. 19. 21. 23.
            25.It cannot be simplified. 27. 29. 31.
         
         
         
         
      
      
      
      
   
   
   
   


2. 
   
   
   
   35. 
       
       
       
       37. 
           
           
           
           39. 
               
               
               
               41. 
                   
               
               
               
               
           
           
           
           
       
       
       
       
   
   
   
   


3. 
   
   
   
   45. 
       
       
       
       47. 24 49. 51. 53.
           55.. Also, and
           , so. Both
           methods give the same answer, and the correct answer can always be
       
       
       
       
   
   
   
   

obtained with either method. 57. 59. 61.^22 63. 5
5

27

4

4

15

232 = 422 28 # 232 = 222 # 422 = 8 # 2 = 16

28 # 232 = 28 # 32 = 2256 = 16 28 = 222

1222 326 6210 1225 3025

2522 5210 622 922 2217

4210 - 1027 923

325 226 3210 523 525

215 222 242 281 , 213 r

- 4.431 23 # 32 23 # 5

• 3 - 4


• 3 - 6

213 22

c^2 = 2 ab+b^2 - 2 ba+a^2 , c^2 =a^2 +b^2.

1 b-a 22 =b^2 - 2 ba+a^2.

c^2.

cL11.705

• 7 - 6 c= 17 b= 8
  
  
  • 8 - 17.321
  
  
  
  

(^233) x (^2) + 4

• 16 -^1211


• 8 - 13 - 145 145 - 30


• 3, 3

c^2 + 2 ab a^2 +b^2 =c^2

1 a+b 22 a^2 + 2 ab+b^2

8

(^115)
(^19529) E (^212) F 5 - 2, 1 6
712 z+ 12
24

• k- 5
  k 1 k+ 121 k- 12

7

151 q- 42

3 r+ 28

7 r

4

q

E5,-^12 , 32 F -^2 -^1

14 x^2 + 1212 x+ 1212 x- 12 5 - 3, 5 6

14 t+ 3 v 212 t+v 2

6 p^2 + 7 p+ 1 +

3

3 y p- 1

(^3) + 8 y (^2) + 12 y- 5
k^2 + 2 k+ 1 4 a^2 - 4 ab+b^2
1
m^6
1
24 x^7
51 - 1, 3 26 0 65. 67. 69.m 71. 73.^6 z 75. 77.

79. 
    
    
    
    81. 
        
        
        
        83. 
            
            
            
            85. 
                
                
                
                87. 
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


80. 
    
    
    
    91. 
        
        
        
        93. 
            
            
            
            95. 
                
                
                
                97. 
                    
                    
                    
                    99. 
                        
                    
                    
                    
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


81. 
    
    
    
    103. 
         
         
         
         105. 
              
              
              
              107. 109.p 111.
              
              
              
              
         
         
         
         
    
    
    
    


82. 
    
    
    
    115. 
         
         
         
         117. 
              
              
              
              119. 121.6 cm 123.6 in.
                   125.D 127. 129.
              
              
              
              
         
         
         
         
    
    
    
    

Section 8.3 (pages 515–516)

1.distributive 3.radicands 5. 7. 9.

11. 
    
    
    
    13. 15.It cannot be added by the distributive
        property. 17. 19. 21. 23.
    
    
    
    


12. 
    
    
    
    27. 
        
        
        
        29. 
            
            
            
            31. 
                
            
            
            
            
        
        
        
        
    
    
    
    


13. 
    
    
    
    35. 
        
        
        
        37. 
            
            
            
            39. 
                
                
                
                41. 
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


14. 
    
    
    
    45. 
        
        
        
        47. 
            
            
            
            49. 
                
                
                
                51. 
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


15. 
    
    
    
    55. 
        
        
        
        57. 
            
            
            
            59. 
                
            
            
            
            
        
        
        
        
    
    
    
    


16. 
    
    
    
    63. 0 65. 67. 5 69. 71. 7
    
    
    
    


17. 14 75. 77. 6 79. 2 81.

Section 8.4 (pages 521–523)

1. 
   
   
   
   3. 
      
      
      
      5. 
         
         
         
         7. 
            
            
            
            9. 
               
               
               
               11. 
                   
               
               
               
               
            
            
            
            
         
         
         
         
      
      
      
      
   
   
   
   


2. 
   
   
   
   15. 
       
       
       
       17. 
           
           
           
           19. 
               
               
               
               21. 
                   
                   
                   
                   23. 
                       
                   
                   
                   
                   
               
               
               
               
           
           
           
           
       
       
       
       
   
   
   
   


3. 
   
   
   
   27. 
       
       
       
       29. 
           
           
           
           31. 
               
               
               
               33. 
                   
               
               
               
               
           
           
           
           
       
       
       
       
   
   
   
   

35.1; identity property for multiplication 37. 39.

41. 
    
    
    
    43. 1 45. 47. 49. 51.
    
    
    
    


42. 
    
    
    
    55. 
        
        
        
        57. 
            
            
            
            59. 
                
                
                
                61. 
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


43. 
    
    
    
    65. 
        
        
        
        67. 69.B 71. 73.
        
        
        
        
    
    
    
    


44. 
    
    
    
    77. 
        
        
        
        79. 
            
            
            
            81. 
                
                
                
                83. 
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


45. 
    
    
    
    87. (a) sec (b)3.182 sec 89.
    
    
    
    


46. 
    
    
    
    93. 
        
    
    
    
    

Section 8.5 (pages 527–529)

1. 13 3. 4 5. 7. 9.


2. 
   
   
   
   13. 
       
       
       
       15. 
           
       
       
       
       
   
   
   
   


3. 
   
   
   
   19. 
       
       
       
       21. 23 23. 1 25. 2
       
       
       
       
   
   
   
   


4. 
   
   
   
   29. 
       
   
   
   
   


5. 
   
   
   
   33. 35.Because multiplication must be performed before addition, it is
       incorrect to add and. Since cannot be simplified, the
       expression cannot be written in a simpler form, and the final answer is
   
   
   
   
   
   
   • 37 - 2215. 37. 49 + 142 x+x
     
     
     • 37 - 2 - 2215
     
     
     
     
   
   
   
   

230 + 215 + 625 + 3210 187 - 20221

223 - 2 + 322 - 26 1522 - 15

37 + 1227 7 + 226

57 + 2326 81 + 14221 71 - 1627

215 - 235 30 + 2210 427

36 x^2 - 1 pa-pm+qa-qm

32 x^2 + 44 x- 21

922

4

242

2

2342 mn^2

6 n

236 y

2 y

23196

7

2350

5

23121

11

232

4

234

2

3 a 25 r

5

x 2 y

2 y

p 22 pm

m

x 27 xy

y

p 23 q

q

42 m

m

23 y

y

26 p

p

423

27

23

5

1722

6

215

10

1

6

3214

4

221

3

265

5

• 25
  5

23

3

2125

5

• 322
  10

325

5

22

8

2230

3

(^3222222)
10
823
9
230
2
8215
5
226
3
(^62525)
5
222 5023

• 24 z 234 z 2222 282

6 k^2 h 26 + 27 hk 26 k 623 p^22124 m^3 - 8 p 24 p

723 r 15 x 23 2 x 22 13 p 23 42 x 25 z

523 - 232 24233 10242 + 4248 22 x

• 222 - 1223 422 323 - 225 3221

823 - 2022 1927 1226 + 625

3217 723

723 - 527 226

• 5 x+ 19 11 x^2 y- 7 xy

m^4

2 t 232 t 2

4 z^27 a^3 b^2

4232 2245 23 - 56 x^3

2235 3232

x^2 y^3

13

y^2

10

27

x^5

9 m^2 n

3 c^725 z^22 z a^62 a 8 x^32 x x^3 y^6

625 254 y^220 x^33 x^422

A-20 Answers to Selected Exercises

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