Rationalizing the Denominator
Definition of Rationalizing the Denominator
- Rationalizing the denominator is the process by which a fraction containing radicals in the denominator is rewritten to have only rational numbers in the denominator.
Examples of Rationalizing the Denominator
In the example above, the radical 
in the denominator is converted into a rational number by multiplying and dividing the fraction by 
using the fact that 
. This process is called ‘rationalizing the denominator.’
Here 
in the denominator is converted into a rational number by multiplying and dividing the fraction by the conjugate 
using the fact that 
.
Solved Example on Rationalizing the Denominator
Simplify 
by rationalizing the denominator.
Choices:
A. 
B. 
C. 
D.
Correct answer: D
Solution:
Step 1: 
[Use quotient property.]
Step 2: 
[Use product property.]
Step 3: 
[
]
Step 4: 
[Multiply by a value of 
= 1.]
Step 5: 
Related Terms for Rationalizing the Denominator
- Denominator
- Rational Number
- Fraction
Additional Links for Rationalizing the Denominator
