Beginning Algebra, 11th Edition

93.Concept Check To help find cube roots, complete this list of perfect cubes.

94.Concept Check To help find fourth roots, complete this list of perfect fourth powers.

Find each root. See Examples 9 and 10.

Use a calculator with a cube root key to find each root. Round to the nearest thousandth.

Write each number in prime factored form. See Section 6.1.

121. 72 122. 100 123. 40 124. 242 125. 23 126. 41

PREVIEW EXERCISES

23 251.8 23 - 87 23 - 95

2312 2374 23 130.6

• 2481 - 24256 25 - 1024 25 - 100,000

241296 24 10,000 24 - 1 24 - 625

• 23 - 8 - 23 - 343 24625 24256

23 - 27 23 - 64 23 - 216 23 - 343

231 2327 23125 231000

64 = 74 = 84 = 94 = 104 =

14 = 24 = 34 = 44 = 54 =

63 = 73 = 83 = 93 = 103 =

13 = 23 = 33 = 43 = 53 =

504 CHAPTER 8 Roots and Radicals

OBJECTIVES OBJECTIVE 1 Multiply square root radicals.In this section, we develop sev-

eral rules for finding products and quotients of radicals. Notice that

and

showing that

This result is a particular case of the product rule for radicals.

24 # 29 = 24 # 9.

24 # 29 = 2 # 3 = 6 24 # 9 = 236 = 6 ,

Multiplying, Dividing, and Simplifying Radicals

8.2

1 Multiply square

root radicals.

2 Simplify radicals by

using the product

rule.

3 Simplify radicals by

using the quotient

rule.

4 Simplify radicals

involving variables.

5 Simplify other roots.

Product Rule for Radicals

For nonnegative real numbers aand b,

and

That is, the product of two square roots is the square root of the product, and the

square root of a product is the product of the two square roots.

2 a# 2 b 2 a#b 2 a#b 2 a# 2 b.

CAUTION In general, To see why this is so, let

and

216 + 9 = 225 = 5 , but 216 + 29 = 4 + 3 = 7.

y=9.

2 x+yZ 2 x+ 2 y. x= 16

http://www.ebook777.com

http://www.ebook777.com