Algebra Demystified 2nd Ed

Chapter 5 e X P O N e N T S a N D r O O T S 119

DeMYSTiFieD / algebra DeMYSTiFieD / HuttenMuller / 000-0 / Chapter 5

Roots of fractions or fractions with a root in the denominator are not simplified.

To eliminate a root in a denominator, we use two facts, naan= and bb= 1. This
process is called rationalizing the denominator. We begin with square roots. If the
denominator is a square root, we multiply the fraction by the denominator over

itself. This forces the new denominator to be in the form a^2.

EXAMPLES

Rationalize the denominator.

1

2

1

2

2

2

2

2

2

(^22)
=⋅==
(^44442)
xx
x
x
x
x
x
x
=⋅==
2
3
2
3
3
3
6
3
6
(^23)
=⋅==
6
2
6
2
2
2
62
2
62
xx^22
x
x
x
x
x
x
=⋅==
()
PRACTICE
Rationalize the denominator.

1.^3
5

=

2.^7
y

=

3.^67 =
4.^8
3

x=

5.^711 xy=
6.^2
10 y

=

EXAMPLES

Rationalize the denominator.

EXAMPLES

Rationalize the denominator.

PRACTICE

Rationalize the denominator.

3

PRACTICE

Rationalize the denominator.