How do you simplify -3sqrt3(2+sqrt6)?

May 22, 2017

$- 6 \sqrt{3} - 9 \sqrt{2}$

Explanation:

First, distribute the $- 3 \sqrt{3}$ to both terms inside parentheses.

$- 3 \sqrt{3} \cdot 2 - 3 \sqrt{3} \cdot \sqrt{6}$

Now simplify.

$- 6 \sqrt{3} - 3 \sqrt{18}$

18 is $2 \times 3 \times 3$.

$- 6 \sqrt{3} - 3 \sqrt{2 \times 3 \times 3}$

You have two factors of 3 inside the radical, so you can pull them out and make one factor of 3 outside the radical.

-6sqrt3-3sqrt(2timescolor(limegreen)3timescolor(limegreen)3

$- 6 \sqrt{3} - 3 \cdot \textcolor{\lim e g r e e n}{3} \sqrt{2}$

Finally, simplify again.

$- 6 \sqrt{3} - 9 \sqrt{2}$

May 22, 2017

$- 6 \sqrt{3} - 9 \sqrt{2}$

Explanation:

Given -

$- 3 \sqrt{3} \left(2 + \sqrt{6}\right)$
$- 6 \sqrt{3} - 3 \sqrt{3} \sqrt{6}$
$- 6 \sqrt{3} - 3 \sqrt{3} \sqrt{3} \sqrt{2}$
$- 6 \sqrt{3} - 3.3 \sqrt{2}$
$- 6 \sqrt{3} - 9 \sqrt{2}$