# Rationalizing the denominator

by Emilee
(USA)

5/((6 + 3√2) - (2 + 2√2))

Rationalize the denominator of 5 over open parentheses 6 plus 3 square root of 2 close parentheses minus open parentheses 2 plus 2 square root of 2 close parentheses:

### Comments for Rationalizing the denominator

 Jan 09, 2013 Remove Radicals from Denominator by: Staff Answer Part I Rationalizing the Denominator is the standard way of simplifying fractions containing radicals in the denominator. Rationalizing the denominator means to “rewrite the fraction so there are no radicals in the denominator”. The technique used to rationalize the denominator of a fraction is always the same: Multiply the original fraction (which contains radicals in the denominator) by another fraction (a / a). To ensure the value of the original fraction (which contains radicals in the denominator) will not change, the second fraction (a / a) will always to equal to 1. The value of the numerator (a) in the second fraction and the value of the denominator (a) in the second fraction will always be the same. The denominator of the new fraction (after multiplication) will contain no radicals. Rationalizing the denominator of any fraction is really a problem of determining what the second fraction should be, so that: = [original fraction] * 1 a = currently unknown expression = [(original numerator) / (original denominator)] * (a / a) = [(original numerator) * a] / [(original denominator) * a] After multiplication is complete, the denominator of the new fraction [(original denominator) * a] will not contain any radicals. [(original denominator) * a] = a value which does not contain radicals ---------------------------------------