# How do you simplify sqrt5 + 3sqrt7 - 4sqrt5 - 5sqrt7?

Jul 28, 2018

$- 3 \sqrt{5} - 2 \sqrt{7}$

#### Explanation:

We can rewrite this as

$\textcolor{s t e e l b l u e}{\sqrt{5} - 4 \sqrt{5}} + \textcolor{p u r p \le}{3 \sqrt{7} - 5 \sqrt{7}}$

We can factor a $\sqrt{5}$ out of the blue terms and a $\sqrt{7}$ out of the purple terms. We now have

$\textcolor{s t e e l b l u e}{\left(1 - 4\right) \sqrt{5}} - \textcolor{p u r p \le}{\left(3 - 5\right) \sqrt{7}}$

$\textcolor{s t e e l b l u e}{- 3 \sqrt{5}} \textcolor{p u r p \le}{- 2 \sqrt{7}}$

Hope this helps!