Unit 7.5 Rationalizing Denominators and Numerators of Radical Expressions
Concepts: Rationalization is a process by which radicals in the denominator or numerator on
a rational expression are eliminated.
Objective 1: Rationalize denominators.
Notes:
Lecture:
To rationalize the
3
x
1.
denominator, multiply
5
y
both the numerator and
denominator by the
radical in the
denominator.
3
6
2. 3
3
9
4
3.
3 25
4x
7x
3y
4.
4
5.
4
x
81y 5
1
Now try yourself!
1.
2.
7
3.
2
5m
11n
2 9
16 y
3
4.
3
z2
27x 4
Objective 2: Rationalize denominators having two terms.
Lecture: Rationalize the denominator
1.
2.
3.
32
2 3
5
3 52
Notes:
Many rational quotients have
a sum or difference of terms
in a denominator, rather than
a single radical.
In that case, we need to
multiply by the conjugate of
the numerator or denominator
(which ever one we are
rationalizing).
The conjugate uses the same
terms, but the opposite
operation (+ or –).
3 x
2 x y
2
Now try yourself!
2
1.
54
Objective 3: Rationalize numerators.
Lecture:
32
1.
2.
3.
4.
80
3
2.
4 x
2 x
Notes:
An expression rewritten
with no radical in the
numerator is called
rationalizing the
numerator.
9y
7
3
5b
3
2a
x 3
4
3
Now try yourself!
1.
2x 7
8
3
2.
3
6x 2
5y
Things to do:
1. Homework in MyMathLab 7.5
4