Question

√a -√b
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√a + √b

Rational the denominator. Assume that all expressions under radicals represent positive numbers.

Answer 1

Rationalizing a denominator means removing all roots from it. To rationalize a denominator with a sum of 2 roots, we multiply the top and bottom of the expression by the difference of the two roots:

\[(\sqrt{a} - \sqrt{b}) / (\sqrt{a} + \sqrt{b}) = \]
\[[\sqrt{a} - \sqrt{b} / \sqrt{a} + \sqrt{b}] *[\sqrt{a} - \sqrt{b} / \sqrt{a} - \sqrt{b}] =\]
\[ (a - b - 2\sqrt{a*b} )/ (a - b)\]