# What is the square root of 360 divided by 640 ?

Apr 23, 2017

$\sqrt{\frac{360}{640}} = \frac{3}{4}$

#### Explanation:

I think what you want is the simplified form of the square root of $\frac{360}{640}$.

If so then first note that if $a , b > 0$ then:

$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

Also, if $a \ge 0$ then:

$\sqrt{{a}^{2}} = a$

So we find:

$\sqrt{\frac{360}{640}} = \sqrt{\frac{{2}^{3} \cdot {3}^{2} \cdot 5}{{2}^{7} \cdot 5}} = \sqrt{{3}^{2} / {2}^{4}} = \frac{\sqrt{{3}^{2}}}{\sqrt{{\left({2}^{2}\right)}^{2}}} = \frac{\sqrt{{3}^{2}}}{\sqrt{{4}^{2}}} = \frac{3}{4}$

Alternatively:

$\sqrt{\frac{360}{640}} = \sqrt{\frac{36 \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{10}}}}{64 \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{10}}}}} = \sqrt{\frac{36}{64}} = \frac{\sqrt{36}}{\sqrt{64}} = \frac{\sqrt{{6}^{2}}}{\sqrt{{8}^{2}}} = \frac{6}{8} = \frac{3}{4}$