# Rationalizing

A fraction is not considered simplified until all the radicals have been removed from the denominator. If a denominator contains a single term with a square root, it can be rationalized by multiplying both the numerator and denominator by that square root. If the denominator contains square roots separated by a plus or minus sign, then multiply both the numerator and denominator by the conjugate, which is formed by merely changing the sign between the roots.

Example

Rationalize the fraction .

Solution

Multiply top and bottom of the fraction by :

Example

Rationalize the fraction .

Solution

Multiply top and bottom of the fraction by the conjugate :