Rationalization of radicals

To rationalize an expression with radicals in the denominator consists in finding an equivalent expression with no roots in the denominator.

To do this we multiply the numerator and the denominator by a suitable expression that eliminates the roots in the denominator.

Example

$\frac{1}{\sqrt{5}} = \frac{1 \cdot \sqrt{5}}{\sqrt{5} \cdot \sqrt{5}} = \frac{\sqrt{5}}{(\sqrt{5})^{2}} = \frac{\sqrt{5}}{5}$