Question
Simplify (2√5+3√7)^2 . Show your work. Justify each step.
Answers
GPT 3.5
To simplify (2√5+3√7)^2, we need to square each term inside the parentheses and then combine like terms.
(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.
(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.