# How do you simplify sqrt(50) - sqrt(18)?

Jun 11, 2018

$2 \sqrt{2}$

#### Explanation:

The key realization here is that we can leverage the radical property

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

Thus, we can rewrite $\textcolor{b l u e}{\sqrt{50}} - \textcolor{red}{\sqrt{18}}$ as

$\textcolor{b l u e}{\sqrt{25 \cdot 2}} - \textcolor{red}{\sqrt{9 \cdot 2}}$

which simplifies to

$5 \sqrt{2} - 3 \sqrt{2}$

Factoring out a $\sqrt{2}$, we get

$\sqrt{2} \left(5 - 3\right)$

Which simplifies to

$2 \sqrt{2}$

Hope this helps!