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# If r > 0, is r^(1/2) an integer?

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Math Expert
Joined: 02 Sep 2009
Posts: 55228
If r > 0, is r^(1/2) an integer?  [#permalink]

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20 Dec 2015, 05:11
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Difficulty:

15% (low)

Question Stats:

79% (00:53) correct 21% (01:04) wrong based on 96 sessions

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If r > 0, is $$\sqrt{r}$$ an integer?

(1) r^2 is an integer.
(2) r = m^2, where m is an integer.

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Re: If r > 0, is r^(1/2) an integer?  [#permalink]

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20 Dec 2015, 05:24
2
(1) r^2 is an integer.

If r = 3 , r^2 = 3^2 = 9 is an integer
(3)^(1/2) is not an integer
r= 4 , r^2 = 4^2 = 16 is an integer
(4)^(1/2) that is 2 is an integer
Not sufficient

(2) r = m^2, where m is an integer.
=> (r)^(1/2) = m
Square root of r will be an integer .
Sufficient

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Re: If r > 0, is r^(1/2) an integer?  [#permalink]

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20 Dec 2015, 05:29
Given, r>0

1. r^2= Integer
Case 1: eg, r^2=25, r = +/-5 but √5 is not integer
Case 2: eg, r^2= 16,r = +/-4 and √4 = +/- 2 is an integer.
Hence Insufficient

2. r=m^2 where m = Int
=> √r = +/- m , which is an Int
Hence B.
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Re: If r > 0, is r^(1/2) an integer?  [#permalink]

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30 Nov 2018, 10:46
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Re: If r > 0, is r^(1/2) an integer?   [#permalink] 30 Nov 2018, 10:46
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