# How do you simplify sqrt10-sqrt5?

Jul 18, 2017

see a solution process below:

#### Explanation:

First, rewrite the radical on the left as:

$\sqrt{2 \cdot 5} - \sqrt{5}$

Next, use this rule for radicals to rewrite the term on the left again:

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

$\sqrt{\textcolor{red}{2} \cdot \textcolor{b l u e}{5}} - \sqrt{5} \implies \sqrt{\textcolor{red}{2}} \sqrt{\textcolor{b l u e}{5}} - \sqrt{5}$

Next, factor out the common terms:

$\sqrt{2} \sqrt{5} - \sqrt{5} \implies \sqrt{2} \sqrt{5} - 1 \sqrt{5} \implies$

$\left(\sqrt{2} - 1\right) \sqrt{5}$