# Rationalization of a Denominator

## Rationalization of a Denominator

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: $$\dfrac{1}{\sqrt{a}}$$ × $$\dfrac{\sqrt{a}}{\sqrt{a}}$$ = $$\dfrac{\sqrt{a}}{a}$$

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: $$\dfrac{8}{\sqrt{7} +\sqrt{3}}$$ × $$\dfrac{\sqrt{7}-\sqrt{3}}{\sqrt{7}-\sqrt{3}}$$ = $$\dfrac{8(\sqrt{7}-\sqrt{3})}{4}$$ = $$2(\sqrt{7}-\sqrt{3})$$