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