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# Is the positive square root of x an integer? 1. x=n^6 and n

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Manager
Joined: 09 Dec 2009
Posts: 120

Kudos [?]: 55 [1], given: 19

Is the positive square root of x an integer? 1. x=n^6 and n [#permalink]

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30 Jul 2010, 10:46
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68% (00:46) correct 32% (01:13) wrong based on 38 sessions

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Is the positive square root of x an integer?

1. x=n^6 and n is an integer
2. x^2 = m and m is an integer
[Reveal] Spoiler: OA

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Round 2: 07/10/10 - This time it's personal.

Kudos [?]: 55 [1], given: 19

Manager
Joined: 20 Mar 2010
Posts: 83

Kudos [?]: 110 [3], given: 1

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30 Jul 2010, 15:57
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1. x=$$n^6$$ . $$\sqrt{x}$$ = +/- $$n^3$$ depending on whether n is +ve or -ve.
Either way since n is an integer , $$n^3$$ is an integer and so is $$\sqrt{x}$$. So 1 is sufficient
2. $$x^2$$ is an integer doesn't require $$\sqrt{x}$$ to be an integer.
$$\sqrt{x}$$ will be an integer when $$x^2$$ =$$1^4,2^4,3^4.......$$
For any other integer $$\sqrt{x}$$ is not an integer. So 2 is not sufficient

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Re: Is the positive square root of x an integer? 1. x=n^6 and n [#permalink]

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01 Aug 2017, 00:47
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Re: Is the positive square root of x an integer? 1. x=n^6 and n   [#permalink] 01 Aug 2017, 00:47
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