How do you multiply (2sqrt7+sqrt5)(sqrt3+sqrt2)(2sqrt7-sqrt5)(27+5)(3+2)(275)?

1 Answer
Jun 5, 2015

It's easiest to multiply (2sqrt(7)+sqrt(5))(2sqrt(7)-sqrt(5))(27+5)(275) first...

(2sqrt(7)+sqrt(5))(2sqrt(7)-sqrt(5))(27+5)(275) is of the form

(a+b)(a-b) = a^2 - b^2(a+b)(ab)=a2b2 with a=2sqrt(7)a=27 and b=sqrt(5)b=5

So:

(2sqrt(7)+sqrt(5))(2sqrt(7)-sqrt(5))(27+5)(275)

=(2sqrt(7))^2-sqrt(5)^2 = (4*7)-5 = 28 - 5 = 23=(27)252=(47)5=285=23

Then

(2sqrt(7)+sqrt(5))(sqrt(3)+sqrt(2))(2sqrt(7)-sqrt(5))(27+5)(3+2)(275)

= (2sqrt(7)+sqrt(5))(2sqrt(7)-sqrt(5))(sqrt(3)+sqrt(2))=(27+5)(275)(3+2)

=23(sqrt(3)+sqrt(2)) = 23sqrt(3)+23sqrt(2)=23(3+2)=233+232