# How do you find the square root of the fraction 64/100?

Sep 4, 2015

Have a look:

#### Explanation:

You can write:
$\sqrt{\frac{64}{100}} = \frac{\sqrt{64}}{\sqrt{100}} =$ and solve the two (exact) roots separately!
So you get:
$\frac{8}{10} = \frac{4}{5}$

Sep 4, 2015

$\frac{64}{100} = \frac{16}{25} = \frac{4 \cdot 4}{5 \cdot 5} = \left(\frac{4}{5}\right) \cdot \left(\frac{4}{5}\right) = {\left(\frac{4}{5}\right)}^{2}$

So $\sqrt{\frac{64}{100}} = \sqrt{{\left(\frac{4}{5}\right)}^{2}} = \frac{4}{5}$

#### Explanation:

In general, if $a \ge 0$ then $\sqrt{{a}^{2}} = a$

Also, if $b > 0$, then $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$, though we did not have to use that this time.