# How do you simplify 1/(sqrt2+sqrt7)?

Jun 21, 2016

$\frac{1}{\sqrt{2} + \sqrt{7}} = \frac{\sqrt{7} - \sqrt{2}}{5}$

#### Explanation:

We simplify $\frac{1}{\sqrt{2} + \sqrt{7}}$ by rationalizing the denominator i.e. multiplying numerator and denominator by conjugate of denominator.

As $\left(\sqrt{2} + \sqrt{7}\right)$ can be written as $\left(\sqrt{7} + \sqrt{2}\right)$ and its conjugate is (sqrt7-sqrt2)#, hence

$\frac{1}{\sqrt{2} + \sqrt{7}} = \frac{1}{\sqrt{7} + \sqrt{2}}$

= $\frac{1 \times \left(\sqrt{7} - \sqrt{2}\right)}{\left(\sqrt{7} + \sqrt{2}\right) \left(\sqrt{7} - \sqrt{2}\right)}$

= $\frac{\sqrt{7} - \sqrt{2}}{7 - 2} = \frac{\sqrt{7} - \sqrt{2}}{5}$