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

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Answer 1 · 2017-05-22T01:23:03

#-6sqrt3-9sqrt2#

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

Answer 2 · 2017-05-22T01:26:01

#-6sqrt3-9sqrt2#

Given -

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