Question

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

Answer 1

Firstly, we use the formula for a binomial square:

(a+b)^2 = a^2 + 2ab + b^2

Here, a = 2sqrt(5) and b = 3sqrt(7), so:

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

= 20 + 12sqrt(35) + 63

= 83 + 12sqrt(35)

Therefore, (2sqrt(5) + 3sqrt(7))^2 = 83 + 12sqrt(35).