How do you evaluate #2\sqrt { 3} ( - 4\sqrt { 2} + \sqrt { 2)) #?

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Answer 1 · 2018-05-26T14:46:02

#-6sqrt(6)#

we have
#-4sqrt(2)+sqrt(2)=-3sqrt(2)#
then
#2sqrt(3)*(-3sqrt(2))=-6sqrt(3)*sqrt(2)=-6sqrt(6)#

Answer 2 · 2018-05-26T14:53:38

#-6sqrt6#

#color(blue)(2sqrt3(-4sqrt2+sqrt2)#

When we add radicals, we should not add the numbers inside the root signs. But, we can add the numbers outside the root signs.

So,

#rarr2sqrt3((-4+1)sqrt2)#

#rarr2sqrt3(-3sqrt2)#

When we multiply radicals, we should multiply both the numbers inside and outside the radicals

#rarr(2)(-3)(sqrt2)(sqrt3)#

#color(green)(rArr-6sqrt6#

Hope that helps...#phi#