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# Is the positive square root of x an integer?

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Math Expert
Joined: 02 Sep 2009
Posts: 52971
Is the positive square root of x an integer?  [#permalink]

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17 Dec 2017, 22:29
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Difficulty:

35% (medium)

Question Stats:

73% (01:38) correct 27% (01:38) 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.

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Joined: 02 Sep 2009
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Re: Is the positive square root of x an integer?  [#permalink]

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17 Dec 2017, 22:30
Bunuel wrote:
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.

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https://gmatclub.com/forum/is-the-posit ... 23921.html
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Re: Is the positive square root of x an integer?  [#permalink]

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17 Dec 2017, 23:10
Bunuel wrote:
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.

(1) n is an integer, n^6 is thus 6th power of an integer. So positive square root of x will be √(n^6) = n^3. Since n is an integer, n^3 is also an integer. Thus positive square root of x is an integer. Sufficient. (here its also important to note that whether n is positive or negative its sixth power will be positive only. and since we are talking about positive square root here, √x will be positive only. So for example, even if n=-2, then n^6=64, and its positive square root will be 8 only, not -8)

(2) So square of x is an integer. But this doesnt mean x is also an integer. It might be (eg, if x is 4) or it might not be (eg, if x is 5). so Insufficient.

Re: Is the positive square root of x an integer?   [#permalink] 17 Dec 2017, 23:10
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