# How do you find 2 sqrt 325?

Sep 9, 2015

Assuming we are dealing with only the principal square root:
$\textcolor{w h i t e}{\text{XXX}} 2 \sqrt{325} = 10 \sqrt{13}$
Using a calculator we could further evaluate this as $36.05551$

#### Explanation:

$325 = 5 \times 5 \times 13$

So
$\textcolor{w h i t e}{\text{XXX}} \sqrt{325} = \sqrt{{5}^{2} \times 13} = \sqrt{{5}^{2}} \cdot \sqrt{13} = 5 \sqrt{13}$
and
$\textcolor{w h i t e}{\text{XXX}} 2 \sqrt{325} = 2 \times 5 \sqrt{13} = 10 \sqrt{13}$

The simplest way to find an approximation for the irrational value $\sqrt{13}$ is to use a calculator.

If we are not restricted to the principal square root then $- 10 \sqrt{13}$ is another solution.