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If n^2 is interger is n an interger

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Source: — Data Sufficiency |
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by netigen » Tue Jun 03, 2008 2:47 pm
May be or may not be

n^2 = 25 then n=5 hence int
n^2 = 3 then n=sqrt(3) hence not an int
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by zacharyz » Tue Jun 03, 2008 6:33 pm
Well, netigen is answering the question that I think you were asking. However, the actual question asked was if n is an integer, is n^2 an integer.

The answer to that is YES. n^2 means that you are multiplying n * n. Since n is an integer, n^2 is always an integer. Look at any examples you want, but that is the definition.

Your original question is one of the tricks that you see on some GMAT questions.

Now, back to what netigen explained, and is good to know in general, if n is an integer, there is no guarantee that sqrt(n) is an integer. If n is a perfect square (1, 4, 16, 25, 36...), then sqrt(n) is an integer. If not, then it is some decimal. Namely:

sqrt(3) ~1.7 and sqrt (2) ~ 1.4
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by s_raizada » Wed Jun 04, 2008 11:54 am
Thanks guys!

Your explanation is simple and I agree with that but OG explanation is wierd. OG 11 DS Q 146
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