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Rationalize Denominators

Rationalize Denominators

MATH 018
Combined Algebra
S. Rook

Overview

• Section 10.5 in the textbook:
– Rationalizing a denominator with one term
– Rationalizing a denominator with two terms

Rationalizing Denominators
with One Term

Rationalizing Denominators with
One Term

• Rationalizing: the process of eliminating the
radical from either the numerator or
denominator of a fraction

– We will only be rationalizing the denominator
Consider

– what happens when we multiply

by itself?

• Thus, we can say:

• To rationalize a denominator with one term:
– Determine what needs to be multiplied to
eliminate the radical in the denominator
– Multiply this term times BOTH the numerator and
denominator (dealing with an expression)
• This eliminates the radical in the denominator
– Acceptable to have radicals present in the
numerator

Simplify Radicals Before
Rationalizing

• Consider rationalizing

– Could multiply numerator and denominator by

– Easier, however to simplify

• Multiply numerator and denominator by

instead of

• See if radicals can be simplified before
rationalizing
– Otherwise radicals must be simplified at the end where
the numbers are larger

Rationalizing Denominators with
One Term (Example)

Ex 1: Rationalize the denominator:

Rationalizing Denominators
with Two Terms

Rationalizing Denominators with
Two Terms

• Again, goal is to eliminate the radicals from
the denominator
– Consider

– Consider

• Conjugate: same 2 terms but different signs
– Given

, what would be its conjugate?
• To rationalize a denominator with two terms:
– Multiply BOTH the numerator and denominator by
the conjugate (dealing with an expression)
• Eliminates the radical(s) in the denominator
– Acceptable to have radicals present in the
numerator

• Look to simplify radicals before rationalizing

Ex 2: Rationalize the denominator:

Summary

• After studying these slides, you should
know how to do the following:

– Rationalize denominators containing one or
two terms

• Additional Practice
– See the list of suggested problems for 10.5

• Next lesson
– Solving Radical Equations (Section 10.6)