Beginning Algebra, 11th Edition

NOTE In Example 1(b),we could also have rationalized the original denominator,

, by multiplying by since

Either approach yields the same correct answer.

OBJECTIVE 2 Write radicals in simplified form.A radical is considered to be

in simplified form if the following three conditions are met.

12

28

=

12 # 22

28 # 22

=

1222

216

=

1222

4

= 322

28 22 , 28 # 22 = 216 =4.

518 CHAPTER 8 Roots and Radicals

Conditions for Simplified Form of a Radical

1. The radicand contains no factor (except 1) that is a perfect square (when
   dealing with square roots), a perfect cube (when dealing with cube roots), and
   so on.


2. The radicand has no fractions.


3. No denominator contains a radical.

Simplifying a Radical

Simplify.

Quotient rule

Rationalize the denominator.

Factor.

Product rule

= Product rule NOW TRY

3215

5

= 29 = 3

3 # 23 # 25

5

=

29 # 23 # 25

5

=

29 # 3 # 25

5

= 25 # 25 = 5

227 # 25

5

=

227 # 25

25 # 25

=

227

25

B

27

5

NOW TRY EXAMPLE 2

EXERCISE 2

Simplify
B

27

7

.

NOW TRY ANSWER

2. 3221
   7

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