Name DateWORKSHEET 7.7: USING CONJUGATES TO SIMPLIFY
RADICAL EXPRESSIONS
-------------------------------------------------------------------------------------If the denominator of a radical expression contains the sum or difference of a number and a
radical, use a conjugate to simplify the expression. A conjugate is an expression with the
opposite operation of the original expression. For example, the expressions 5 +√
3 and
5 −√
3 are conjugates. Follow the steps below to use conjugates to simplify radical
expressions:- Identify the conjugate of the expression in the denominator.
- Multiply the numerator and denominator by the conjugate.
- Simplify the product.
EXAMPLE
Simplify3
2 +
√
3
.
2 −
√
3 is the conjugate of the expression in the denominator.3
2 +√
3
·
2 −
√
3
2 −
√
3
3(2−
√
3)
(2+
√
3)(2−
√
3)
=
6 − 3
√
3
4 − 2
√
3 + 2
√
3 −
√
9
=
6 − 3
√
3
4 − 3
6 − 3
√
3
1
= 6 − 3
√
3
DIRECTIONS: Simplify each expression.
2
4 +
√
3
5
7 −
√
5
10
5 +
√
2
15
√
7 − 5
4
3
√
2 − 10
3
4 − 7
√
3
CHALLENGE:Explain why multiplying by a conjugate eliminates the radical
sign.265Copyright
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.