Rationalizing Numerators and
Denominators of Radical
Expressions
8.5
Rationalizing Denominators
You may not have a radical in the
denominator.
Example:
8
5
Nor may you have a fraction in a radical.
2
Example:
3
Simplifying Fractions with a Radical in
the Denominator (Numerator)
In short, multiply the denominator by the
smallest value to make the denominator a
perfect nth root.
“To rationalize a denominator containing a single nth
root, multiply the fraction by a well chosen “1” so that the
product’s denominator has a radicand that is a perfect nth
power.”
Examples
a.
8
5
b.
2
3
c.
3
6 x y3
9 x3 y
3
7
2
16x
d.
Sums/Differences in
Denominator
Some radicals have either a sum or
difference in the denominator.
Examples:
7
3 5
12 5
11
3
Simplifying with Sums/Differences
in the Denominator
Multiply the numerator and denominator
by the conjugate of the denominator.
“To rationalize a denominator containing a sum or
difference with at least one square root term,
multiply the fraction by a 1 whose numerator and
denominator are the conjugate of the denominator.”
Examples
a.
7
3 5
b.
12 5
11
3
c.
4
x 3
Rationalizing Numerators and
Denominators of Radical
Expressions
8.5