Intermediate Algebra
Section 7.5 – Rationalizing Radical Expressions
When dividing radical expressions, we do not want radicals in the
denominator. The process of eliminating a radical in a denominator
is called rationalizing the denominator.
A radical expression is in simplest form when all three of the
statements below are true:
1. All possible nth powered factors have been removed from
each radical.
2. No radical contains a fraction.
3. All denominators have been rationalized.
Example:
a)
5
15
Rationalize each denominator.
Section 7.5 – Rationalizing Rational Functions
b)
c)
d)
12
28
3
3
16x
4a
4
12a 3
page 2
Section 7.5 – Rationalizing Rational Functions
Recall, when dealing with radical expressions, the terms
page 3
a+ b
and a − b are called conjugates. To rationalize a denominator
with two terms in the denominator, multiply the numerator and
denominator of the radical expression by the conjugate of the
denominator.
Example:
a)
3
7 −4
b)
9
3− 3
Rationalize each denominator.
Section 7.5 – Rationalizing Rational Functions
Example:
Add.
3
2
+
8
2
page 4