Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Simplify
(2√5+3√7)^2
. Show your work. Justify each step.
To simplify (2√5+3√7)^2, we will first use the rule (a+b)^2 = a^2 + 2ab + b^2.
So,
(2√5+3√7)^2
= (2√5)^2 + 2(2√5)(3√7) + (3√7)^2
= 4(5) + 2(2)(3)(√5)(√7) + 9(7)
= 20 + 24√35 + 63
= 83 + 24√35
Therefore, (2√5+3√7)^2 simplifies to 83 + 24√35.