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

Mar 10, 2018

$\frac{- 5 \sqrt{14}}{14}$

Explanation:

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

$\therefore \frac{\sqrt{7}}{\sqrt{7}} = 1$ and $\frac{\sqrt{2}}{\sqrt{2}} = 1$

$\therefore = \frac{\sqrt{7}}{\sqrt{7}} \times \frac{\sqrt{2}}{\sqrt{7}} - \frac{\sqrt{7}}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}$

$\therefore \sqrt{7} \times \sqrt{7} = 7$ and $\sqrt{2} \times \sqrt{2} = 2$

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

$\therefore = \frac{2 \left(\sqrt{2} \sqrt{7}\right) - 7 \left(\sqrt{2} \sqrt{7}\right)}{14}$

$\therefore = \frac{- 5 \sqrt{2} \sqrt{7}}{14}$

$\therefore = \frac{- 5 \sqrt{14}}{14}$