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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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25% (medium)

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65% (00:33) correct 35% (00:31) wrong based on 1101 sessions

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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

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15 May 2010, 03:05
5
6
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
2
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]

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11 Jun 2018, 13:44
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?

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

pushpitkc, is my approach correct ?

$$\sqrt{2} = 1.4$$

$$\sqrt{5}=2.2$$

$$2.2+1.4 = 3.6$$

$$(3.6)^2 = 12.96$$ apprx $$13$$
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Of the following integers which is the closest approximation  [#permalink]

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11 Jun 2018, 13:47
1
dave13 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?

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

pushpitkc, is my approach correct ?

$$\sqrt{2} = 1.4$$

$$\sqrt{5}=2.2$$

$$2.2+1.4 = 3.6$$

$$(3.6)^2 = 12.96$$ apprx $$13$$

Yes dave13 - that approach is 100% correct!
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Of the following integers which is the closest approximation &nbs [#permalink] 11 Jun 2018, 13:47
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