Explain in one or two sentences why multiplying the numerator and denominator of by…

MATHEMATICS · Subjective · AoPS · Mathematics · Special Factorizations · Special Factorizations

Problem

Explain in one or two sentences why multiplying the numerator and denominator of

\dfrac{1}{\sqrt{a}+\sqrt{b}}

\sqrt{a}-\sqrt{b}

removes the radicals from the denominator.