# How do you simplify sqrt8/sqrt7?

Aug 12, 2016

$\frac{2 \sqrt{14}}{7}$

#### Explanation:

It is not good maths practice to leave a radical in the denominator.

We can "rationalize the denominator" which means changing it from an irrational to a rational number.

$\frac{\sqrt{8}}{\sqrt{7}} = \frac{\sqrt{8}}{\sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}} \text{ because } \frac{\sqrt{7}}{\sqrt{7}} = 1$

$\frac{\sqrt{8}}{\sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}} = \frac{\sqrt{8 \times 7}}{7} \text{ } {\sqrt{7}}^{2} = 7$

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

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