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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 :


 





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