Question 136727
{{{(sqrt(6)+2sqrt(2))(4sqrt(6)-3sqrt(2))}}}


Use FOIL just like you would on something like {{{(x-2)(x+4)}}}


First: {{{sqrt(6)*4sqrt(6)=4*6=24}}}


Outside: {{{sqrt(6)*-3sqrt(2)=-3sqrt(12)=-3*2sqrt(3)=-6sqrt(3)}}}


Inside: {{{2sqrt(2)*4sqrt(6)=8sqrt(12)=8*2sqrt(3)=16sqrt(3)}}}


Last: {{{2sqrt(2)*-3sqrt(2)=-6*2=-12}}}


Add 'em up:
{{{24-6sqrt(3)+16sqrt(3)-12}}}
{{{12+10sqrt(3)}}}


{{{sqrt(81x^12y^8z^10)}}}


Remember that {{{sqrt(x)=x^(1/2)}}}, and {{{x^(m/n)=root(n,x^m)}}}


so


{{{sqrt(81x^12y^8z^10)=9x^6y^4z^5}}}