# How do you simplify sqrt14-sqrt(2/7)?

Nov 10, 2015

$\frac{6}{7} \cdot \sqrt{14}$

#### Explanation:

$\sqrt{14} - \sqrt{\frac{2}{7}} = \sqrt{14} - \frac{\sqrt{2}}{\sqrt{7}} = \sqrt{14} \cdot \frac{\sqrt{7}}{\sqrt{7}} - \frac{\sqrt{2}}{\sqrt{7}}$

$= \frac{\sqrt{14} \cdot \sqrt{7} - \sqrt{2}}{\sqrt{7}} = \frac{\sqrt{2 \cdot 7 \cdot 7} - \sqrt{2}}{\sqrt{7}}$

$= \frac{\sqrt{2} \cdot 7 - \sqrt{2}}{\sqrt{7}} = \frac{\sqrt{2} \cdot 6}{\sqrt{7}}$

If you would like to eliminate the radical in the denominator, you might want to take a few more steps:

$\frac{\sqrt{2} \cdot 6}{\sqrt{7}} = \frac{\sqrt{2} \cdot 6}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}} = \frac{\sqrt{2} \cdot \sqrt{7} \cdot 6}{7} = \frac{6}{7} \cdot \sqrt{14}$