# How do you simplify sqrt(12/75)?

Jun 10, 2018

$\frac{2}{5}$

#### Explanation:

We can leverage the radical property

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

All this is saying is that the square root of the quotient is the same as the quotient of the square roots. We can now rewrite our expression as

$\frac{\textcolor{b l u e}{\sqrt{12}}}{\textcolor{p u r p \le}{\sqrt{75}}}$

This is equivalent to

$\frac{\textcolor{b l u e}{\left(\sqrt{4} \cdot \sqrt{3}\right)}}{\textcolor{p u r p \le}{\left(\sqrt{25} \cdot \sqrt{3}\right)}}$

Since we have a $\sqrt{3}$ on the top and bottom, these cancel:

$\frac{\sqrt{4} \cdot \cancel{\sqrt{3}}}{\sqrt{25} \cdot \cancel{\sqrt{3}}}$

And we're left with

$\frac{\sqrt{4}}{\sqrt{25}}$

Which simplifies to

$\frac{2}{5}$

Hope this helps!