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#(sqrt2+2sqrt8)(3sqrt6-sqrt5)#

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Answer 1 · 2018-02-21T03:50:56

Using the F.O.I.L. method and simplifying roots along the way, we get: #30sqrt(3)-5sqrt(10)#

Utilize the F.O.I.L. method:
F irsts
O utsides
I nsides
L asts

Firsts:

#sqrt(2)*3sqrt(6)=3sqrt(2*6)=3sqrt(12)# (Recall that #sqrt(a)*sqrt(b)=sqrt(ab)# )

#3sqrt(12)=(3)(sqrt(4))(sqrt(3))=(3)(2)sqrt(3)=6sqrt(3)#

Outsides:

#sqrt(2)*(-sqrt(5))=-sqrt(10)#

Insides:

#2sqrt(8)*3sqrt(6)=6sqrt(48)=(6)(sqrt(16))(sqrt(3))=(4)(6)sqrt(3)=24sqrt(3)#

Lasts:

#2sqrt(8)*(-sqrt(5))=-2sqrt(40)=-2sqrt(4)sqrt(10)=(-2)(2)sqrt(10)=-4sqrt(10)#

Add up all of the terms together , and you have your result:

#6sqrt(3)-sqrt(10)+24sqrt(3)-4sqrt(10)#

#30sqrt(3)-5sqrt(10)#