Name DateWORKSHEET 7.3: RATIONALIZING THE DENOMINATOR
-------------------------------------------------------------------------------------Sometimes writing an expression in simplest form requires rationalizing the denominator.
Follow the steps below to rationalize the denominator:- Multiply the numerator and denominator by the radical in the denominator.
- Multiply fractions.
- Simplify the radical.
- Simplify the fraction.
EXAMPLE
3
√
123
√
12·
√
12
√
12
=
3
√
12
√
144
=
3
√
12
12
=
3
√
4
√
3
12
=
3 · 2
√
3
12
=
6
√
3
12
=
√
3
2
DIRECTIONS: Simplify each expression.
5
√
7
4
√
8
10
√
6
2
√
10
√
3
√
5
√
3
√
7
√
5
√
8
−
√
9
√
3
√
8
√
3
√
3
√
11
√
5
√
10
√
12
2
CHALLENGE:Give an example of an expression that contains a radical in the
denominator that can be simplified without rationalizing the denominator.257Copyright
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.