Beginning Algebra, 11th Edition

25. 
    
    
    
    26. 
        
    
    
    
    


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    28. 
        
    
    
    
    


27. 
    
    
    
    30. 
        
    
    
    
    


28. 
    
    
    
    32. 
        
    
    
    
    


29. 
    
    
    
    34. 35.Concept Check In Example 1(b),a student simplified by combining the
        and the to get , which is incorrect.WHAT WENT WRONG?
        36.Concept Check Find each product mentally.
        (a) (b)
    
    
    
    

Simplify each radical expression. See Examples 1–3.

37. 
    
    
    
    38. 
        
    
    
    
    


38. 
    
    
    
    40. 
        
    
    
    
    


39. 
    
    
    
    42. 43.Concept Check Determine the expression by which you should multiply the numerator
        and denominator to rationalize each denominator.
    
    
    
    

(a) (b)

44.Concept Check If you try to rationalize the denominator of by multiplying by

, what problem arises? By what should you multiply?

Rationalize each denominator. Write quotients in lowest terms. See Example 4.

45. 
    
    
    
    46. 
        
        
        
        47. 
            
            
            
            48. 
                
            
            
            
            
        
        
        
        
    
    
    
    


46. 
    
    
    
    50. 
        
        
        
        51. 
            
            
            
            52. 
                
            
            
            
            
        
        
        
        
    
    
    
    


47. 
    
    
    
    54. 
        
        
        
        55. 
            
            
            
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48. 
    
    
    
    58. 
        
        
        
        59. 
            
            
            
            60. 
                
            
            
            
            
        
        
        
        
    
    
    
    


49. 
    
    
    
    62. 
        
        
        
        63. 
            
            
            
            64. 
                
            
            
            
            
        
        
        
        
    
    
    
    


50. 
    
    
    
    66. 
        
        
        
        67. 
            
            
            
            68. 
                
            
            
            
            
        
        
        
        
    
    
    
    

Write each quotient in lowest terms. See Example 5.

69. 
    
    
    
    70. 
        
        
        
        71. 
            
            
            
            72. 
                
            
            
            
            
        
        
        
        
    
    
    
    


70. 
    
    
    
    74. 
        
        
        
        75. 
            
            
            
            76. 
                
            
            
            
            
        
        
        
        
    
    
    
    

25 + 275

10

16 + 2128

24

9 - 622

12

12 - 2210

4

426 + 6

10

223 + 10

8

625 - 9

3

527 - 10

5

2

2 x- 2 y

1

2 x+ 2 y

12

6 + 2 y

8

4 - 2 x

928

622 - 6

2108

3 + 323

23

22 + 23

25

22 + 23

26 + 25

23 + 25

27 + 22

23 - 22

322 - 4

23 + 2

226 + 1

22 + 5

3 + 22

22 + 1

6 - 25

22 + 2

25 + 2

2 - 23

22 + 3

23 - 1

223

2 - 210

223

23 + 5

218

22 - 1

212

23 + 1

38

5 - 26

7

2 - 211

1

4 + 215

1

2 + 25

4 + 23

4 + 23

2

4 + 23

3

26 - 25

1

25 + 23

A 23 m+ 22 nBA 23 m- 22 nB A 24 p- 23 kBA 24 p+ 23 kB

A 32 t + 27 BA 22 t - 214 B A 22 z- 23 BA 2 z- 25 B

A^12 -^2 rB

2

A^7 +^2 xB

2

A 2 x+ 2 yBA 2 x- 2 yB A 228 - 214 BA 228 + 214 B

• 37 - 2 - 39215
  
  
  • 37 - 2215
  
  
  
  

A^822 -^323 B

2

A^527 -^223 B

2

A^25 +^230 BA^26 +^23 B A^210 -^220 BA^22 -^25 B

A 210 - 25 BA 25 + 220 B A 26 - 23 BA 23 + 218 B

A 22 + 23 BA 26 - 22 B A 23 + 25 BA 215 - 25 B

A^278 -^276 BA^278 +^276 B A^285 -^282 BA^285 +^282 B

528 CHAPTER 8 Roots and Radicals

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