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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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New post 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

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Re: Roots  [#permalink]

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New post 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?


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

Answer: C.
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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: 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
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?


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

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
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 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

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

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New post 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?


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

Answer: C.



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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New post 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?


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

Answer: C.



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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