How do you simplify #(3sqrt3 - 4sqrt2)(2sqrt3 + 4sqrt2)#?

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Answer 1 · 2016-09-10T13:11:51

#=4sqrt6 -14#

Recall: #sqrtx xx sqrtx = sqrt(x^2) = (sqrtx)^2 = x#

and #sqrt x xx sqrty = sqrt(xy)#

Each term in the first bracket must be multiplied by each term in the second bracket. This will give 4 terms, which might simplify.

#(3sqrt3 - 4sqrt2)(2sqrt3 + 4sqrt2)#

=#6xx3 +12sqrt6-8sqrt6 -16xx2#

=#18+4sqrt6-32#

#=4sqrt6 -14#