# How do you simplify sqrt52-sqrt1300?

Jun 6, 2017

See a solution process below:

#### Explanation:

We can rewrite the terms within the radicals as:

$\sqrt{4 \cdot 13} - \sqrt{4 \cdot 325}$

Using this rule for multiplication of radicals we can rewrite each radical as:

$\sqrt{\textcolor{red}{a} \cdot \textcolor{b l u e}{b}} = \sqrt{\textcolor{red}{a}} \cdot \sqrt{\textcolor{b l u e}{b}}$

$\sqrt{\textcolor{red}{4} \cdot \textcolor{b l u e}{13}} - \sqrt{\textcolor{red}{4} \cdot \textcolor{b l u e}{325}} = \left(\sqrt{\textcolor{red}{4}} \cdot \sqrt{\textcolor{b l u e}{13}}\right) - \left(\sqrt{\textcolor{red}{4}} \cdot \sqrt{\textcolor{b l u e}{325}}\right) =$

sqrt(color(red)(4))(sqrt(color(blue)(13)) - sqrt(color(blue)(325))) = 2(sqrt(13) - sqrt(325)

We can now simplify the radical on the right as:

$2 \left(\sqrt{13} - \sqrt{\textcolor{red}{25} \cdot \textcolor{b l u e}{13}}\right) = 2 \left(\sqrt{13} - \left(\sqrt{\textcolor{red}{25}} \cdot \sqrt{\textcolor{b l u e}{13}}\right)\right) =$

$2 \left(\sqrt{13} - 5 \sqrt{\textcolor{b l u e}{13}}\right) = 2 \sqrt{13} \left(1 - 5\right) = 2 \sqrt{13} \cdot - 4 =$

$- 8 \sqrt{13}$

Or

$- 28.8$ rounded to the nearest 10th