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Of the following integers which is the closest approximation

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vannbj
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Of the following integers which is the closest approximation [#permalink] 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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Bunuel
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Of the following integers which is the closest approximation [#permalink] New post  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?


\((\sqrt{2} + \sqrt{5})^2=2+2*\sqrt{2}*\sqrt{5}+5=7+2\sqrt{10}\)

Since \(\sqrt{10}\approx{3}\), then \(7+2\sqrt{10}\approx{7+6}=13\)

Answer: C.­­­
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Bunuel
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Re: Of the following integers which is the closest approximation [#permalink] New post  30 Mar 2015, 05:15
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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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Re: Numbers [#permalink] New post  23 Apr 2013, 01:35
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\((a+b)^2=(2+5+2\sqrt{10})=2+5+2*3=13\)

C
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Re: Of the following integers which is the closest approximation [#permalink] New post  30 Mar 2015, 05:11
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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] New post  31 Mar 2015, 12:14
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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] New post  18 Dec 2017, 08:45
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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] New post  11 Jun 2018, 13:44
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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] New post  11 Jun 2018, 13:47
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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xabi14
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Re: Of the following integers which is the closest approximation [#permalink] New post  25 Feb 2021, 22:11
In which circumstances do we use (a+b)^2 = a^2 + 2ab + b^2 rather than a^2 + b^2?
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Bunuel
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Of the following integers which is the closest approximation [#permalink] New post  26 Feb 2021, 00:19
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xabi14 wrote:
In which circumstances do we use (a+b)^2 = a^2 + 2ab + b^2 rather than a^2 + b^2?


(a + b)^2 always equals to a^2 + 2ab + b^2. Or did you mean something else?
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Re: Of the following integers which is the closest approximation [#permalink] New post  26 Feb 2021, 01:50
Bunuel wrote:
xabi14 wrote:
In which circumstances do we use (a+b)^2 = a^2 + 2ab + b^2 rather than a^2 + b^2?


(a + b)^2 always equals to a^2 + 2ab + b^2. Or did you mean something else?


Thought a^2 + b^2, like a^2 + 2ab + b^2, was also an equivalent to (a+b)^2. That's why i ended up with choice A.
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Re: Of the following integers which is the closest approximation [#permalink] New post  26 Feb 2021, 01:55
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xabi14 wrote:
Bunuel wrote:
xabi14 wrote:
In which circumstances do we use (a+b)^2 = a^2 + 2ab + b^2 rather than a^2 + b^2?


(a + b)^2 always equals to a^2 + 2ab + b^2. Or did you mean something else?


Thought a^2 + b^2, like a^2 + 2ab + b^2, was also an equivalent to (a+b)^2. That's why i ended up with choice A.


No.

\((a + b)^2 = (a + b)(a + b) = a^2 + ab + ab + b^2 = a^2 + 2ab + b^2\)


7. Algebra



For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
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Re: Of the following integers which is the closest approximation [#permalink] New post  28 Feb 2021, 03:14
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Solution



Given
The expression \((√2+√5)^2\)

To find
We need to determine
    • The approximate value of this expression

Approach and Working out

    • \((√2+√5)^2\)
      o \(= (√2)^2 + (√5)^2 + 2(√2) (√5)\) [using the identity \((a+b)^2 = a^2 + b^2 + 2ab\)]
      o = 2 + 5 + 2√10
      o = 7 + 2√10
         √10 is approximately equal to √9, which is equal to 3.
         So, 7 + 2√10 is approximately equal to 7 + 2(3)
          • = 7 + 6
          • = 13

Thus, option C is the correct answer.

Correct Answer: Option C
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Of the following integers which is the closest approximation [#permalink] New post  29 May 2023, 05:32
Because the question says "approximate", that's exactly what I did.

√2 ≈ 1.4
√5 ≈ 2.2

(1.4+2.2)^2 = (3.6)^2

(3.6)^2 must lie between 3^2 and 4^2.

3^2 = 9
4^2 = 16

Also note that 3.6 is closer to 4 than it is to 3. Therefore, (3.6)^2 must also lie closer to 4^2 than it does to 3^2.

Only 13 satisfies this condition. Therefore, C is the answer.
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Of the following integers which is the closest approximation [#permalink]
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