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Of the following integers which is the closest approximation

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Of the following integers which is the closest approximation [#permalink]

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

A. 7
B. 10
C. 13
D. 15
E. 17
[Reveal] Spoiler: OA

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Re: Roots [#permalink]

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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.
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Numbers [#permalink]

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New post 23 Apr 2013, 01:14
Of the following integers what is the closest approximation to ( squareroot 2 + squareroot 5 )^ 2 ?

1.7
2.10
3.13
4.15
5.17
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Re: Numbers [#permalink]

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New post 23 Apr 2013, 01:35
\((a+b)^2=(2+5+2\sqrt{10})=2+5+2*3=13\)

C
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Re: Numbers [#permalink]

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New post 23 Apr 2013, 04:48
Expert's post
kabilank87 wrote:
Of the following integers what is the closest approximation to ( squareroot 2 + squareroot 5 )^ 2 ?

1.7
2.10
3.13
4.15
5.17


Merging similar topics.

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Re: Of the following integers which is the closest approximation [#permalink]

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Re: Of the following integers which is the closest approximation [#permalink]

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New post 30 Mar 2015, 05:11
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
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Re: Of the following integers which is the closest approximation [#permalink]

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New post 30 Mar 2015, 05:15
Expert's post
joaomario wrote:
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


I'm not exactly sure what you are doing there...

You should apply \((a+b)^2=a^2+2ab+b^2\).

Hope it helps.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Of the following integers which is the closest approximation [#permalink]

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New post 31 Mar 2015, 12:14
Expert's post
vannbj wrote:
Of the following integers, which is the closest approximation to \((\sqrt{2} + \sqrt{5})^2\)?

A. 7
B. 10
C. 13
D. 15
E. 17

(sqrt(2) + sqrt(5))^2 =2 + 2*sqrt(2)*sqrt(5) + 5
= 7 + 2*sqrt(10)
= 7 + 2*3 (approximated to sqrt(9))
= 13
Hence option (C).

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Re: Of the following integers which is the closest approximation [#permalink]

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New post 16 May 2016, 08:01
Hello from the GMAT Club BumpBot!

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Re: Of the following integers which is the closest approximation   [#permalink] 16 May 2016, 08:01
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