Which of the following is the best approximation?

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Which of the following is the best approximation? [#permalink]

11 Oct 2012, 12:56

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Question Stats:

76% (01:22) correct

24% (00:45) wrong

based on 4 sessions

(\sqrt{2}+\sqrt{5})^2 which of the following is the best approximation?
a. 7
b. 10
c. 13
d. 15
e. 17

Is there somebody who could explain how to make this calculate quickly?
I find this question in the Gmat prep software, what is the level of the question?

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Re: which of the following is the best approximation? [#permalink]

11 Oct 2012, 13:03

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IanSolo wrote:

(\sqrt{2}+\sqrt{5})^2 which of the following is the best approximation?
a. 7
b. 10
c. 13
d. 15
e. 17

The right answer is c.
Is there somebody who could explain how to make this calculate quickly?
I find this question in the Gmat prep software, what is the level of the question?

(a+b)^2=a^2+2ab+b^2, thus (\sqrt{2}+\sqrt{5})^2=2+2*\sqrt{2}*\sqrt{5}+5=7+2\sqrt{10}.

Now, 3^2=9, so \sqrt{10} is a little bit greater than 3, which means that 7+2\sqrt{10}\approx{7+2*3}=13.

Answer: C.

P.S. I'd say it's ~600 level question.
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Re: Which of the following is the best approximation? [#permalink]

10 Dec 2012, 23:36

(\sqrt{2}+\sqrt{5})(\sqrt{2}+\sqrt{5})
2 + \sqrt{10 + [square_root]10} + 5[/square_root]
7 + 2\sqrt{10}

\sqrt{9} = 3
\sqrt{16} = 4
[fraction]10[/fraction] - a little more than 3

7 + 2*3 = 7 + 6 ~ 13

Answer: 13

Re: Which of the following is the best approximation? [#permalink] 10 Dec 2012, 23:36

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Which of the following is the best approximation?

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Which of the following is the best approximation?

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