Beginning Algebra, 11th Edition

Find each product and simplify. See Example 3.

55.Simplify the product in two ways. First, multiply 8 by 32 and simplify
the square root of this product. Second, simplify , simplify , and then multiply.
How do the answers compare? Make a conjecture (an educated guess) about whether the
correct answer can always be obtained using either method when simplifying a product
such as this.

56.Simplify the radical in two ways. First, factor 288 as and then simplify.
Second, factor 288 as and then simplify. How do the answers compare? Make a
conjecture concerning the quickest way to simplify such a radical.

Simplify each radical expression. See Examples 4 – 6.

Simplify each radical. Assume that all variables represent nonnegative real numbers. See
Example 7.

69. 
    
    
    
    70. 
        
        
        
        71. 
            
            
            
            72. 
                
            
            
            
            
        
        
        
        
    
    
    
    


70. 
    
    
    
    74. 
        
        
        
        75. 
            
            
            
            76. 
                
            
            
            
            
        
        
        
        
    
    
    
    


71. 
    
    
    
    78. 
        
        
        
        79. 
            
            
            
            80. 
                
            
            
            
            
        
        
        
        
    
    
    
    


72. 
    
    
    
    82. 
        
        
        
        83. 
            
            
            
            84. 
                
            
            
            
            
        
        
        
        
    
    
    
    


73. 
    
    
    
    86. 
        
        
        
        87. 
            
            
            
            88. 
                
            
            
            
            
        
        
        
        
    
    
    
    


74. 
    
    
    
    90. 
        
        
        
        91. , 92. ,
        
        
        
        
    
    
    
    


75. 
    
    
    
    94. 
        
        
        
        95. 
            
            
            
            96. B
            
            
            
            
        
        
        
        
    
    
    
    

w^8 z^10

B^400

x^4 y^6

B^169

w^8

B^144

y^4

100

zZ 0

B

14

z^12

xZ 0

B

7

x^10

281 m^4 n^22100 c^4 d^6

264 x^7225 t^112 x^6 y^122 a^8 b^10

2 z^52 y^32 a^132 p^17

218 x^8220 r^10245 c^14250 d^20

236 z^2249 n^22400 x^62900 y^8

2 m^22 k^22 y^42 s^4

B

8

3

#

B

512

B 27

5

2

#

B

125

8

50220

2210

30210

522

2200

22

275

B 23

14

B 72

4

50

B

13

B 25

7

B 16

9

B 100

16

225

48 # 6

2288 144 # 2

28 232

28 # 232

526 # 2210 523 # 2215 426 # 322

212 # 230 230 # 224 2210 # 322

23 # 221 212 # 248 250 # 272

29 # 232 29 # 250 23 # 218

SECTION 8.2 Multiplying, Dividing, and Simplifying Radicals 511

x

y

(–6, 5)

(3, – 4)

(^0) x
y
(–2, 4)
(^0) (4, 0)
x
y
(–5, –1)
(3, 1)
0 x
y
(– 4, –5)
(3, – 4)
0
Use the distance formula to find the length of each line segment. Express answers as simpli-
fied radicals. See Section 8.1.