Question

simplify (2√5+3√7)^2

Justify your answer

I posted this with no answer earlier. I hope i can get one now

Answer 1

Remember that \((a + b)^2 = a^2 + 2ab + b^2\).

Answer 2

It's the same as:
\[(2\sqrt{5} +3\sqrt{7})*(2\sqrt{5} +3\sqrt{7})\]
Just multiply it out

Answer 3

Okay, thanks

Answer 4

It should be:
\[4(5)+6(\sqrt{35})+6(\sqrt{35})+9(7)\]
Now just simplify

Answer 5

20 + 36 + 36 + 63 = 155. Answer?

Answer 6

Actually it be \[83+12\sqrt{35}\]

Answer 7

oh.. so then whats the answer? Or is that the answer?

Answer 8

That's the answer.

Answer 9

@HatSimulator How did you get to 20 + 36 + 36 + 63?

Also, @Luigi0210 's step can be further simplified using my identity.

Answer 10

Wait, you sure?

Answer 11

@Luigi0210 Yes. Do you need proof?

Answer 12

I'd like proof

Answer 13

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