# How do you simplify (-5sqrt6)(2sqrt3)?

May 24, 2017

$\left(- 5 \sqrt{6}\right) \left(2 \sqrt{3}\right) = - 30 \sqrt{2}$

#### Explanation:

$\left(- 5 \sqrt{6}\right) \left(2 \sqrt{3}\right)$

= $\left(- 5\right) \times \sqrt{6} \times 2 \times \sqrt{3}$

= $- \left(5 \times 2 \times \sqrt{6} \times \sqrt{3}\right)$

= $- \left(10 \times \sqrt{6 \times 3}\right)$

= $- \left(10 \times \sqrt{2 \times \underline{3 \times 3}}\right)$

= $- 10 \times 3 \times \sqrt{2}$

= $- 30 \sqrt{2}$

May 26, 2017

$- 30 \sqrt{2}$

#### Explanation:

This is all one term made of factors multiplied together.

$\textcolor{w h i t e}{\ldots \ldots \ldots} - 5 \times \textcolor{b l u e}{\sqrt{6}} \times 2 \times \sqrt{3}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots .} \downarrow$
$= - 5 \times \textcolor{b l u e}{\sqrt{2} \times \sqrt{3}} \times 2 \times \sqrt{3} \text{ } \leftarrow$ now re-arrange

$= \textcolor{g r e e n}{- 5 \times 2} \times \textcolor{red}{\sqrt{3} \times \sqrt{3}} \times \sqrt{2}$

$= \textcolor{g r e e n}{- 10} \times \textcolor{red}{3} \times \sqrt{2}$

$= - 30 \sqrt{2}$

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Remember that:

$\textcolor{red}{\sqrt{3} \times \sqrt{3} = {\textcolor{red}{\sqrt{3}}}^{2} = 3}$