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

1 answer

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

First, we will use the distributive property to expand the expression:
(2sqrt(5) + 3sqrt(7)) * (2sqrt(5) + 3sqrt(7))

= (2sqrt(5))^2 + 2 * 2 * sqrt(5) * 3 * sqrt(7) + (3sqrt(7))^2
= 4 * 5 + 12sqrt(35) + 9 * 7
= 20 + 12sqrt(35) + 63
= 83 + 12sqrt(35)

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