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

2 Answers
May 22, 2017

-6sqrt3-9sqrt2

Explanation:

First, distribute the -3sqrt3 to both terms inside parentheses.

-3sqrt3*2-3sqrt3*sqrt6

Now simplify.

-6sqrt3-3sqrt18

18 is 2 times 3 times 3.

-6sqrt3-3sqrt(2times3times3)

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

-6sqrt3-3*color(limegreen)3sqrt2

Finally, simplify again.

-6sqrt3-9sqrt2

Final Answer

May 22, 2017

-6sqrt3-9sqrt2

Explanation:

Given -

-3sqrt3(2+sqrt6)
-6sqrt3-3sqrt3sqrt6
-6sqrt3-3sqrt(3)sqrt3sqrt2
-6sqrt3-3.3sqrt2
-6sqrt3-9sqrt2