Simplify (2\sqrt(5)+3\sqrt(7))^(2). Show your work. Justify each step.

Answer 1

To simplify (2√5 + 3√7)^2, we will use the formula for a binomial squared:

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

In this case, a = 2√5 and b = 3√7. So, we have:

(2√5 + 3√7)^2 = (2√5)^2 + 2(2√5)(3√7) + (3√7)^2.

Simplify each term:

= 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).