# How do you simplify -3sqrt18+3sqrt8-sqrt24?

Aug 11, 2016

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

#### Explanation:

Find each number as the product of its prime factors and see what we are working with. Factors in pairs have a square root.

$- 3 \sqrt{18} + 3 \sqrt{8} - \sqrt{24}$

=$- 3 \sqrt{\left(3 \times 3\right) \times 2} + 3 \sqrt{\left(2 \times 2\right) \times 2} - \sqrt{\left(2 \times 2\right) \times 2 \times 3}$

=$- 3 \times 3 \textcolor{red}{\sqrt{2}} + 3 \times 2 \textcolor{red}{\sqrt{2}} - 2 \textcolor{red}{\sqrt{2}} \sqrt{3}$

There is a common factor, factorise:

=$\textcolor{red}{\sqrt{2}} \left(- 9 + 6 - 2 \sqrt{3}\right)$

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