Beginning Algebra, 11th Edition

Using Conjugates to Rationalize Denominators Simplify by rationalizing each denominator. Assume that

(a)

= Subtract.

(^5) A 3 - (^25) B
4

= 32 =9; A 25 B^2 = 5

(^5) A 3 - (^25) B
9 - 5
= 1 x+y 21 x-y 2 =x^2 - y^2

5 A 3 - 25 B

32 - A (^25) B^2

=

(^5) A 3 - (^25) B
A 3 + (^25) BA 3 - (^25) B

5

3 + 25

xÚ0.

EXAMPLE 4

526 CHAPTER 8 Roots and Radicals

(b)

FOIL;

Combine like terms.

x

y=

x
= y

- 1122 - 32

23

=

1122 + 32

- 23

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

622 + 30 + 2 + 522

2 - 25

=

A 6 + 22 BA 22 + 5 B

A^22 -^5 BA^22 +^5 B

6 + 2

2 - 5

(c)

Multiply by.

= 32 =9; A 2 xB^2 =x NOW TRY

(^4) A 3 - 2 xB
9 - x
3 - 2 x= 1
3 - 2 x

=

4 A 3 - 2 xB

A^3 +^2 xBA 3 - 2 xB

4

3 + 2 x

Multiply the numerator and denominator by the conjugate of the denominator.

NOW TRY
EXERCISE 4
Simplify by rationalizing each
denominator. Assume that
.

(a) (b)

(c) kZ 36

9 2 k- 6

,

5 + 27 27 - 2

6 4 + 23

kÚ 0

NOW TRY ANSWERS

(a)