Copyright © Cengage Learning. All rights reserved.
1
9.4 Multiplying and Dividing Radical Expressions
Copyright © Cengage Learning. All rights reserved.
2
What You Will Learn
 Use the Distributive Property or the FOIL
Method to multiply radical expressions.
 Determine the products of conjugates.
 Simplify quotients involving radicals by
rationalizing the denominators.
3
Multiplying Rational Expressions
4
Example 1 – Multiplying Radical Expressions
Find each product and simplify.
Solution
5
Conjugates
6
Conjugates
The expressions
of each other.
and
are called conjugates
Notice that they differ only in the sign between the terms.
The product of two conjugates is the difference of two
squares, which is given by the special product formula
.
7
Example 4 – Multiplying Conjugates
8
Example 5 – Multiplying Conjugates
Find the conjugate of each expression and multiply each
expression by its conjugate.
Solution
a. The conjugate of 2 –
(2 –
)(2 +
is 2 +
) = 22 –
= 4 – 5 = –1
.
Special product formula
Simplify.
9
Example 5 – Multiplying Conjugates
cont’d
b. The conjugate of
is
Special product formula
= 3 – x, x  0
Simplify.
10
Dividing Radical Expressions
11
Dividing Radical Expressions
To simplify a quotient involving radicals, you rationalize the
denominator.
For single-term denominators, you can use the rationalization
process.
To rationalize a denominator involving two terms, multiply
both the numerator and denominator by the conjugate of the
denominator.
12
Example 6 – Simplifying Quotients Involving Radicals
Simplify (a)
and (b)
Solution
Multiply numerator and denominator by
conjugate of denominator.
Special product formula
Simplify.
13
Example 6 – Simplifying Quotients Involving Radicals
cont’d
Simplify.
Multiply numerator and denominator by
conjugate of denominator.
Special product formula
Simplify.
Simplify.
14