Beginning Algebra, 11th Edition

Simplify each radical. Assume that all variables represent positive real numbers. See

Example 4.

53. 
    
    
    
    54. 
        
        
        
        55. 
            
            
            
            56. 
                
            
            
            
            
        
        
        
        
    
    
    
    


54. 
    
    
    
    58. 
        
        
        
        59. 
            
            
            
            60. 
                
            
            
            
            
        
        
        
        
    
    
    
    


55. 
    
    
    
    62. 
        
        
        
        63. 
            
            
            
            64. 
                
            
            
            
            
        
        
        
        
    
    
    
    


56. 
    
    
    
    66. 
        
        
        
        67. 
            
            
            
            68. 
                
            
            
            
            
        
        
        
        
    
    
    
    

69.Concept Check Which one of the following would be an appropriate choice for multiply-

ing the numerator and the denominator of in order to rationalize the denominator?

A. B. C. D.

70.Concept Check In Example 5(b),we multiplied the numerator and denominator of

by to rationalize the denominator. Suppose we had chosen to multiply by in-

stead. Would we have obtained the correct answer after all simplifications were done?

Rationalize each denominator. Assume that variables in denominators are nonzero. See

Example 5.

71. 
    
    
    
    72. 
        
        
        
        73. 
            
            
            
            74. 
                
            
            
            
            
        
        
        
        
    
    
    
    


72. 
    
    
    
    76. 
        
        
        
        77. 
            
            
            
            78. 
                
            
            
            
            
        
        
        
        
    
    
    
    


73. 
    
    
    
    80. 
        
        
        
        81. 
            
            
            
            82. 
                
            
            
            
            
        
        
        
        
    
    
    
    


74. 
    
    
    
    84. 
        
        
        
        85. 
            
            
            
            86. 
                
            
            
            
            
        
        
        
        
    
    
    
    

In Exercises 87 and 88, (a)give the answer as a simplified radical and (b)use a calculator to

give the answer correct to the nearest thousandth.

87.The period pof a pendulum is the time it takes for it to swing from

one extreme to the other and back again. The value of pin seconds is

given by

,

where Lis the length of the pendulum, gis the acceleration due to gravity, and kis a

constant. Find the period when , ft, and ft per sec^2.

88.The velocity vof a meteor approaching Earth is given by

kilometers per second, where dis the distance of the meteor

from the center of Earth and kis a constant. What is the veloc-

ity of a meteor that is 6000 km away from the center of Earth

if ?k= 450

v=

k

2 d

k= 6 L= 9 g= 32

p=k#

B

L

g

B

4

1

B 27

4

1

8

2311 p

2349 q

237 m

2336 n

B

3

3

B 25 x^2

3

3

4 y^2

235

2310

234

237

B

3

4

B^9

3

2

B^5

3

3

B^2

3

1

11

B

3

1

B^5

3

1

B^32

3

1

B^4

3

1

2

232 2316

233

234

235 2325 232 233

232

235

B

2 x^2 z^4

B 3 y

9 a^2 r

B 5

m^2 n

B 2

x^2

4 y

B

a^3 b

B 6

6 p^3

3 m

24 r^3

2 s

27 x^3

2 y

25 a^3

2 b

23 p^2

B 2 q

2 z^2

B x

16

m

B

9

B k

3

B y

5

B x

6

p

522 CHAPTER 8 Roots and Radicals

L

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