# What is (the square root of 7)- 5/(the square root of 2) + 5?

Jun 20, 2018

$\implies - \frac{26 + \sqrt{14} - 5 \sqrt{2} - 5 \sqrt{7}}{23}$

#### Explanation:

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

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

$\implies \frac{\sqrt{14} - 5 \sqrt{2} - 5 \sqrt{7} + 25}{2 - 25}$

$\implies - \frac{26 + \sqrt{14} - 5 \sqrt{2} - 5 \sqrt{7}}{23}$