Question

how do you simplify the square root of a - the square root of b over the square root of a + the square root of b?

Answer 1

\[\frac{\sqrt{a} - \sqrt{b}}{\sqrt{a} + \sqrt{b}}\]

try multiplying the numerator and denominator by
\[\sqrt{a} - \sqrt{b}\]

Answer 2

As suggested above, we use one of the most powerful ideas in math to simplify this one: multiply by one. The form of one we choose will multiply the denominator by its conjugate, which will in turn rationalize the denominator. Recall that (a+b)(a-b)=a^2-b^2. That is the key fact that will simplify this problem.

Answer 3

Continuing...\[\frac{\sqrt{a}-\sqrt{b} }{\sqrt{a}+\sqrt{b}}=\frac{\sqrt{a}-\sqrt{b} }{\sqrt{a}+\sqrt{b}}\frac{\sqrt{a}-\sqrt{b}}{\sqrt{a}-\sqrt{b}}=\frac{a+b-2\sqrt{ab}}{a-b}\]

Answer 4

It is considered bad form to have radicals in the denominator. This method solves that problem.