# How do you rationalize sqrt(10/7)?

May 21, 2015

The answer is $\frac{\sqrt{70}}{7}$ .

Problem: Rationalize $\sqrt{\frac{10}{7}}$ .

$\sqrt{\frac{10}{7}} = \frac{\sqrt{10}}{\sqrt{7}}$

Multiply the numerator and denominator times $\sqrt{7}$.

$\frac{\sqrt{10}}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}$ =

$\frac{\sqrt{10} \sqrt{7}}{7}$

Simplify.

$\frac{\sqrt{70}}{7}$