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Of the following, which is most nearly equal to √10?

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anujtsingh
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Of the following, which is most nearly equal to √10? [#permalink] New post   22 Mar 2013, 12:54
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Of the following, which is most nearly equal to √10?


A. 3.1
B. 3.2
C. 3.3
D. 3.4
E. 3.5
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B
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johnwesley
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Of the following, which is most nearly equal to √10? [#permalink] New post   23 Mar 2013, 07:35
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Just make quick trials:

I would try first 3.3 x 3.3 = 990 + 99 (and put two decimals) = 10.89

Then 3.2 x 3.2 = 960 + 64 (and put two decimals) = 10.24 ---> near to 10

Then 3.1 x 3.1 = 930 + 31 (and put two decimals) = 9.61

Solution: 3.2

Answer: B
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Of the following, which is most nearly equal to √10? [#permalink] New post   22 Feb 2015, 05:13
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anujtsingh wrote:
Of the following, which is most nearly equal to √10?

A. 3.1
B. 3.2
C. 3.3
D. 3.4
E. 3.5


Let us simply take squares of all options.
3.1 * 3.1 = 9.61
3.2 * 3.2 = 10.24
Since it has already crossed 10 (i.e. the square of √10), we need not go further and need to decide between 3.1 and 3.2
10 - 9.61 = 0.39
10.24 - 10 = 0.24
Since 0.24 is lesser of the both, so 3.2 is closer.
Hence (B).

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Of the following, which is most nearly equal to √10? [#permalink] New post   21 Feb 2015, 20:37
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anujtsingh wrote:
Of the following, which is most nearly equal to √10?

A. 3.1
B. 3.2
C. 3.3
D. 3.4
E. 3.5




Square root of 10 can be written as square root of 5 times square root of 2. Square root of 5=2.23 and square root of 2 is 1.41 - multiply these together and the answer you get is closest to 3.2.
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Of the following, which is most nearly equal to √10? [#permalink] New post   26 Jan 2019, 05:01
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I have a super effective alternative approach:

We know that the next bigger perfect square is \(16\) and we can express each option as \((4-x)^2\).
Now, the -ve part of this binomial has to \(≥6\), as \(16-6=10\) hence we can solve the following inequality:

\(2*4*x≥6\) \(\implies\) \(x≥\frac{6}{8}\) \(\implies\) \(x≥0.75\)

The answer closest to \((4-.75)\) is B. Done.
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Re: Of the following, which is most nearly equal to √10? [#permalink] New post   08 Oct 2019, 10:22
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anujtsingh wrote:
Of the following, which is most nearly equal to √10?

A. 3.1
B. 3.2
C. 3.3
D. 3.4
E. 3.5


√10 = √2 * √5
√2 ≈ 1.4 √5 ≈ 2.25 [note: important thing here is we're rounding 1 up and the other down to keep the approximation close]
1.4 * 2.25 = 2.25 + (0.4 * 2.25)
= 2.25 + .9
= 3.15, closer to B
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Of the following, which is most nearly equal to √10? [#permalink] New post   05 Dec 2019, 16:04
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The square roots go up in increments of .2 to .3 roughly
Root 2 = 1.4
Root 3 = 1.7
Root 4 = 2
Root 5 = 2.2
Root 6 = 2.4
Root 7 = 2.6
Root 8 = Root 4*Root 2= 2*root 2 = 2*1.4 = 2.8
Root 9 = 3
Root 10 = 3.2
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Re: Of the following, which is most nearly equal to √10? [#permalink] New post   24 Mar 2013, 04:03
Now take the square of 3.1i.e, 3.1X3.1= 9.64
Now the next number has to be closer to 10
You can check by taking the square of 3.3 and then zero down on 3.2!
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Re: Of the following, which is most nearly equal to √10? [#permalink] New post   13 Oct 2019, 17:22
ghnlrug wrote:
I have a super effective alternative approach:

We know that the next bigger perfect square is \(16\) and we can express each option as \((4-x)^2\).
Now, the -ve part of this binomial has to \(≥6\), as \(16-6=10\) hence we can solve the following inequality:

\(2*4*x≥6\) \(\implies\) \(x≥\frac{6}{8}\) \(\implies\) \(x≥0.75\)

The answer closest to \((4-.75)\) is B. Done.



Can you please elaborate?
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Re: Of the following, which is most nearly equal to √10? [#permalink] New post   05 Dec 2019, 20:25
I find the answer in this way. Difference between\(\sqrt{ 9 }\) and \(\sqrt{16}\) is 1. 1 / (16-9) = 1/7 = 0.142. So\(\sqrt{ 10 }\) will be a little greater than 3.1. So I choose B.
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Re: Of the following, which is most nearly equal to √10? [#permalink] New post   27 Dec 2019, 02:21
I think the best is just to compare 31*31 with 32*32

We already know that it has to be very close to three so it's between those two:

31*31 - 961
32*32 - 1024

Answer choice 3.2
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Re: Of the following, which is most nearly equal to 10? [#permalink] New post   25 May 2023, 04:14
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