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# A question regarding factors of perfect square

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Intern
Joined: 04 Aug 2009
Posts: 10

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A question regarding factors of perfect square [#permalink]

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29 Aug 2010, 11:23
If we are given that a perfect square say x^2 is divisible by n (a non perfect square integer) then it is always true that x^2 = k* n^2?

Is it always true?

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Manager
Joined: 25 Jun 2010
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Re: A question regarding factors of perfect square [#permalink]

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29 Aug 2010, 11:59
What if x=9 and n= 27 ?
Then k will be fractional.

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GMAT Tutor
Joined: 24 Jun 2008
Posts: 1339

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Re: A question regarding factors of perfect square [#permalink]

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29 Aug 2010, 14:53
If we are given that a perfect square say x^2 is divisible by n (a non perfect square integer) then it is always true that x^2 = k* n^2?

Is it always true?

No, that is not always true, at least if you mean for k to be an integer. If you take x^2 = 16, say, then x^2 is divisible by 8, but not by 8^2.

It *is* however true when n is prime. That is, if x is an integer, and x^2 is divisible by a prime p, then x^2 is certainly divisible by p^2.
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Re: A question regarding factors of perfect square   [#permalink] 29 Aug 2010, 14:53
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