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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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14 May 2010, 08:34
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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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15 May 2010, 03:05
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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?

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

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

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

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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?

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

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

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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30 Mar 2015, 05:15
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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?

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

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

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

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31 Mar 2015, 12:14
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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18 Dec 2017, 08:45
Quote:
Of the following integers, which is the closest approximation to $$(\sqrt{2} + \sqrt{5})^2$$?

7
10
13
15
17

We can FOIL (√2 + √5)^2 as (√2 + √5)(√2 + √5):

(√2 + √5)(√2 + √5)

= (√2)^2 + 2(√2)(√5) + (√5)^2

= 2 + 2(√10) + 5

≈ 7 + 2(3)

= 13

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Re: Of the following integers which is the closest approximation   [#permalink] 18 Dec 2017, 08:45
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