# How do you simplify -6sqrt80 + 2sqrt75 - 8sqrt245 - 14sqrt108?

Jul 15, 2017

See a solution process below:

#### Explanation:

$- 6 \sqrt{16 \cdot 5} + 2 \sqrt{25 \cdot 3} - 8 \sqrt{49 \cdot 5} - 14 \sqrt{36 \cdot 3}$

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

$- 6 \sqrt{\textcolor{red}{16} \cdot \textcolor{b l u e}{5}} + 2 \sqrt{\textcolor{red}{25} \cdot \textcolor{b l u e}{3}} - 8 \sqrt{\textcolor{red}{49} \cdot \textcolor{b l u e}{5}} - 14 \sqrt{\textcolor{red}{36} \cdot \textcolor{b l u e}{3}} \implies$

$- 6 \sqrt{\textcolor{red}{16}} \sqrt{\textcolor{b l u e}{5}} + 2 \sqrt{\textcolor{red}{25}} \sqrt{\textcolor{b l u e}{3}} - 8 \sqrt{\textcolor{red}{49}} \sqrt{\textcolor{b l u e}{5}} - 14 \sqrt{\textcolor{red}{36}} \sqrt{\textcolor{b l u e}{3}} \implies$

$\left(- 6 \cdot 4 \sqrt{\textcolor{b l u e}{5}}\right) + \left(2 \cdot 5 \sqrt{\textcolor{b l u e}{3}}\right) - \left(8 \cdot 7 \sqrt{\textcolor{b l u e}{5}}\right) - \left(14 \cdot 6 \sqrt{\textcolor{b l u e}{3}}\right) \implies$

$- 24 \sqrt{\textcolor{b l u e}{5}} + 10 \sqrt{\textcolor{b l u e}{3}} - 56 \sqrt{\textcolor{b l u e}{5}} - 84 \sqrt{\textcolor{b l u e}{3}}$

Then group and combine like terms:

$- 24 \sqrt{\textcolor{b l u e}{5}} - 56 \sqrt{\textcolor{b l u e}{5}} + 10 \sqrt{\textcolor{b l u e}{3}} - 84 \sqrt{\textcolor{b l u e}{3}} \implies$

$\left(- 24 - 56\right) \sqrt{5} + \left(10 - 84\right) \sqrt{3} \implies$

$- 80 \sqrt{5} + \left(- 74\right) \sqrt{3} \implies$

$- 80 \sqrt{5} - 74 \sqrt{3}$