How do you multiply #(2sqrt7+sqrt5)(sqrt3+sqrt2)(2sqrt7-sqrt5)#?

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Answer 1 · 2015-06-05T23:19:31

It's easiest to multiply #(2sqrt(7)+sqrt(5))(2sqrt(7)-sqrt(5))# first...

#(2sqrt(7)+sqrt(5))(2sqrt(7)-sqrt(5))# is of the form

#(a+b)(a-b) = a^2 - b^2# with #a=2sqrt(7)# and #b=sqrt(5)#

So:

#(2sqrt(7)+sqrt(5))(2sqrt(7)-sqrt(5))#

#=(2sqrt(7))^2-sqrt(5)^2 = (4*7)-5 = 28 - 5 = 23#

Then

#(2sqrt(7)+sqrt(5))(sqrt(3)+sqrt(2))(2sqrt(7)-sqrt(5))#

#= (2sqrt(7)+sqrt(5))(2sqrt(7)-sqrt(5))(sqrt(3)+sqrt(2))#

#=23(sqrt(3)+sqrt(2)) = 23sqrt(3)+23sqrt(2)#