# What is the square root of 125/2?

It is $\sqrt{\frac{125}{2}} = \sqrt{{5}^{3} / 2} = 5 \cdot \frac{\sqrt{5}}{\sqrt{2}}$

Sep 21, 2015

$\frac{5 \sqrt{10}}{2}$

#### Explanation:

Start by factoring 125.
$\sqrt{\frac{125}{2}}$
$= \sqrt{\frac{5 \cdot 5 \cdot 5}{2}}$
$= \sqrt{\frac{{5}^{3}}{2}}$

You can already see here that you can bring 5 out.
$\sqrt{\frac{{5}^{3}}{2}}$
$= 5 \sqrt{\frac{5}{2}}$

You can rewrite this as:
$\frac{5 \sqrt{5}}{\sqrt{2}}$

We now need to rationalize this. We can do that by multiplying both the numerator and denominator by a radical that will eliminate the radical in the denominator. In this case, that radical is $\sqrt{2}$.
$\frac{5 \sqrt{5}}{\sqrt{2}}$
$= \frac{5 \sqrt{5}}{\sqrt{2}} \left(\frac{\sqrt{2}}{\sqrt{2}}\right)$
$= \frac{5 \sqrt{5} \cdot \sqrt{2}}{2}$
$= \frac{5 \sqrt{10}}{2}$

You won't be able to simplify it any further. :)