# How do you divide sqrt(36/49)?

Mar 30, 2015

You may have noticed that $36 = {6}^{2}$ and $49 = {7}^{2}$

Squares against square roots cancel out, so:

$\sqrt{\frac{36}{49}} = \sqrt{{6}^{2} / {7}^{2}} = \sqrt{{\left(\frac{6}{7}\right)}^{2}} = \frac{6}{7}$

Another way:

$\sqrt{\frac{36}{49}} = \frac{\sqrt{36}}{\sqrt{49}} = \frac{\sqrt{{6}^{2}}}{\sqrt{{7}^{2}}} = \frac{6}{7}$