# How do you simplify 3/(sqrt7-sqrt2)?

Jul 19, 2018

$\frac{3}{5} \left(\sqrt{7} + \sqrt{2}\right)$

#### Explanation:

By rationalising the denominator which means that you multiply by the conjugate of your denominator

ie the denominator is $\sqrt{7} - \sqrt{2}$ so the conjugate of the denominator is $\sqrt{7} + \sqrt{2}$

$\frac{3}{\sqrt{7} - \sqrt{2}}$

=$\frac{3}{\sqrt{7} - \sqrt{2}} \times \frac{\sqrt{7} + \sqrt{2}}{\sqrt{7} + \sqrt{2}}$

=$\frac{3 \left(\sqrt{7} + \sqrt{2}\right)}{7 - 2}$

=$\frac{3}{5} \left(\sqrt{7} + \sqrt{2}\right)$