Intermediate Algebra (11th edition)

from page 460

Multiply.

= Multiply.

3234

4

=^3234238 = 2

2 # 2

=

3234

2238

=

3 # 234

2232 # 234

3

2232

B^32716 =

3

2232

SECTION 8.5 Multiplying and Dividing Radical Expressions 461

NOW TRY
EXERCISE 4
Simplify.

(a)

(b) xÚ0, y 70
B

4

7 x

y

,

B

3

8

81

Multiply by in numerator

and denominator. This will give

238 = 2 in the denominator.

234

(b)

Quotient rule

Multiply by 1.

Product rule

=

245 xz^3

z

, xÚ0, z 70

=

245 xz^3

24 z^4

=

245 x

24 z

#^24 z

3

24 z^3

=

245 x

24 z

B

4

5 x

z

NOW TRY

OBJECTIVE 3 Rationalize denominators with binomials involving radicals.

Recall the special product To rationalize a denominator

that contains a binomial expression (one that contains exactly two terms) involving

radicals, such as

we must use conjugates.The conjugate of is. In general,

and are x- y conjugates.

1 + 22 1 - 22 x+y

3

1 + 22

,

1 x+ y 21 x- y 2 = x^2 - y^2.

will give ^4 z^4.

^4 z#^4 z^3

CAUTION In Example 4(a),a typical error is to multiply the numerator and

denominator by forgetting that which does notequal 2. We

need threefactors of 2 to obtain under the radical.

232 # 232 # 232 = 2323 which does equal 2.

23

232 , 232 # 232 = 2322 ,

Rationalizing a Binomial Denominator

Whenever a radical expression has a sum or difference with square root radicals

in the denominator, rationalize the denominator by multiplying both the numera-

tor and denominator by the conjugate of the denominator.

NOW TRY ANSWERS

4. (a) (b)

247 xy^3

y

2239

9