The easiest type of expression does not require us to simplify square roots. For example:

\(\dfrac{3}{\sqrt{2}} = \dfrac{3}{\sqrt{2}} \cdot \dfrac{\sqrt{2}}{\sqrt{2}} = \dfrac{3\sqrt{2}}{2}\)The next level of difficulty has expressions where simplification of square roots is necessary. Factors may or may not cancel. For example:

\(\dfrac{5}{\sqrt{50}} = \dfrac{5}{5\sqrt{2}} = \dfrac{1}{\sqrt{2}} \cdot \dfrac{\sqrt{2}}{\sqrt{2}} = \dfrac{\sqrt{2}}{2}\)Rationalize the denominator:

\(\dfrac{6}{\sqrt{2}}\)

\(\dfrac{2}{\sqrt{6}}\)

\(\dfrac{21}{\sqrt{7}}\)

\(\dfrac{\sqrt{2}}{\sqrt{27}}\)

\(\dfrac{\sqrt{5}}{\sqrt{18}}\)

\(\dfrac{1 + \sqrt{7}}{\sqrt{3}}\)

\(\dfrac{\sqrt{3} - 2}{\sqrt{5}}\)

\(\dfrac{3\sqrt{2}}{\sqrt{10}}\)

\(\dfrac{9\sqrt{12}}{2\sqrt{18}}\)