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