Rationalize the Denominator

If the denominator of an otherwise "simplified" radical expression should contain an irrational number (a radical that cannot be simplified), then it is necessary that the denominator be changed to a rational number.  This modification is called "rationalizing the denominator."
For example, if we were to simplify the following problem with the following result, then the radical expression would not be "fully simplified" because there is a radical left in the denominator.

Example 1:
                                  ... Notice that the result contains a radical in the denominator
 

To "rationalize" the denominator multiply the denominator by so that to maintain the equality of the fraction.  So now we would have

                                  ... Now the fraction is "fully simplified"

 

Example 2:

                                    ... Notice that the numerator is also a radical, so multiply under
                                                                  the radical to simplify the numerator
 

Example 3:

            ... Simplify the numerator and denominator
                                                                                     and then rationalize the denominator
 

General Algebra Tips

The views and opinions expressed in this page are strictly those of Mary Lou Baker.
The contents of this page have not been reviewed or approved by Columbia State Community College.

This page was edited on 15-Nov-2007