Method that can be used to convert the irrational denominator of certain fractional expressions into a rational number.

Consider the expression: \(\dfrac{1}{\sqrt{a}}\)

Therefore, we obtain: \(\dfrac{1}{\sqrt{a}}\) × \(\dfrac{\sqrt{a}}{\sqrt{a}}\) = \(\dfrac{\sqrt{a}}{a}\)

Therefore, we obtain: \(\dfrac{1}{\sqrt{a}}\) × \(\dfrac{\sqrt{a}}{\sqrt{a}}\) = \(\dfrac{\sqrt{a}}{a}\)

Consider the expression: \(\dfrac{1}{\sqrt{a} +\sqrt{b}}\)

Therefore, we obtain: \(\dfrac{1}{\sqrt{a} +\sqrt{b}}\) × \(\dfrac{\sqrt{a}-\sqrt{b}}{\sqrt{a}-\sqrt{b}}\) = \(\dfrac{\sqrt{a}-\sqrt{b}}{a-b}\)

### Examples

Consider the expression: \(\dfrac{36}{\sqrt{6}}\)

Therefore, we obtain: \(\dfrac{36}{\sqrt{6}}\) × \(\dfrac{\sqrt{6}}{\sqrt{6}}\) = \(\dfrac{36\sqrt{6}}{6}\) = 6\(\sqrt{6}\)

Consider the expression: \(\dfrac{8}{\sqrt{7} +\sqrt{3}}\)

Therefore, we obtain: \(\dfrac{8}{\sqrt{7} +\sqrt{3}}\) × \(\dfrac{\sqrt{7}-\sqrt{3}}{\sqrt{7}-\sqrt{3}}\) = \(\dfrac{8(\sqrt{7}-\sqrt{3})}{4}\) = \(2(\sqrt{7}-\sqrt{3})\)