Bunuel wrote:

vannbj wrote:

Of the following integers, which is the closest approximation to \((\sqrt{2} + \sqrt{5})^2\)?

7

10

13

15

17

How do you do this without a calculator?

\((\sqrt{2} + \sqrt{5})^2=2+2*\sqrt{2}*\sqrt{5}+5=7+2\sqrt{10}\) --> \(\sqrt{10}\approx{3}\) --> \(7+2\sqrt{10}\approx{7+6}=13\)

Answer: C.

How did you get 2[square_root]10? I expanded the original equation and went from [square_root]20 to 2[square_root]5.

Thanks for your help

More specifically this is how I approached it:

2 + [square_root]10 + [square_root]10 + 5

7 + [square_root]20

7 + [square_root]4 [square_root]5

7 + 2[square_root]5

9 + [square_root]5