Question

(2sqrt(5)+3sqrt(7))^2

Show work.

Answer 1

To square the expression, we can use the formula (a+b)^2 = a^2 + 2ab + b^2:

(2sqrt(5) + 3sqrt(7))^2
= (2sqrt(5))^2 + 2(2sqrt(5))(3sqrt(7)) + (3sqrt(7))^2
= 20 + 12sqrt(35) + 21
= 41 + 12sqrt(35)

Therefore, (2sqrt(5) + 3sqrt(7))^2 = 41 + 12sqrt(35).