Beginning Algebra, 11th Edition

510 CHAPTER 8 Roots and Radicals

(c)

Factor; is a perfect cube.

Product rule

(d)

Quotient rule

= Take cube roots. NOW TRY

y

5

=

23 y^3

23125

B

3

y^3

125

= 2 a 234 a 12 a 23 = 8 a^3

= 238 a^3 # 234 a

= 238 a^3 # 4 a 8 a^3

EXERCISE 9NOW TRY^2332 a^4
Simplify each radical.

(a) (b)

(c) (d)

NOW TRY ANSWERS

9. (a) (b) 4 t

(c) (d)

x^5

2 a 10

(^2235) a
x^4
B
3
x^15
1000
2340 a^7
23 x^122364 t^3
Complete solution available
on the Video Resources on DVD
8.2 EXERCISES
Find each product. See Example 1.

1. 
   
   
   
   2. 
      
      
      
      3. 
         
      
      
      
      
   
   
   
   


2. 
   
   
   
   5. 
      
      
      
      6. 
         
      
      
      
      
   
   
   
   


3. 
   
   
   
   8. 
      
      
      
      9. 
         
      
      
      
      
   
   
   
   


4. 
   
   
   
   11. , 12. ,
       13.Which one of the following radicals is simplified? See Example 2.
       A. B. C. D.
       14.Concept Check If pis a prime number, is in simplified form?
   
   
   
   

Simplify each radical. See Example 2.

Use the Pythagorean theorem to find the length of the unknown side of each right triangle.

Express answers as simplified radicals. See Section 8.1.

3227 928 5250 6240

2160 2128 - 2700 - 2600

2125 280 2145 2110

290 256 275 218

245 227 224 244

2 p

247 245 248 244

217 # 217 213 # 2 r rÚ 0 219 # 2 k kÚ 0

23 # 227 22 # 28 213 # 213

22 # 215 26 # 27 25 # 26

23 # 25 23 # 27 22 # 211

c

(^139)
c
12
10
(^11) b
7
a
9
7
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