Generally, you don't want to have radical at the denominators. So, let's say that we want to simplify the expression \frac{\sqrt{a}}{\sqrt{b}}, where a and b can be any expression you want. Since, of course, \frac{\sqrt{b}}{\sqrt{b}}=1, we can multiply it without changing the value of our expression, so we have \frac{\sqrt{a}}{\sqrt{b}}=\frac{\sqrt{a}}{\sqrt{b}} \cdot \frac{\sqrt{b}}{\sqrt{b}}. The advantage is that now we observe that \sqrt{b} \cdot \sqrt{b}=b, and so our expression becomes \frac{\sqrt{ab}}{b}, and we got rid of the radical at the denominator.
