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# If d is a positive integer, is d^1/2 an integer?

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Re: If d is a positive integer, is d^1/2 an integer? [#permalink]
A.) d = x^2
Therefore, root[d] = x
e.g. d= 16 then root[d] = 4

SUFFICIENT

B.) root[d] = x^2
square of an integer is an integer
e.g. 2^2 = 4, 3^2 = 9
e.g root[d] = 2^2 = 4

SUFFICIENT

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Re: If d is a positive integer, is d^1/2 an integer? [#permalink]
Here is another way of attacking this question. This different approach applies mostly to statement 2.

d is a positive integer, is (d^1/2) an integer?
rephrased, is d a perfect square?

1) d=x^2
square root of x^2 will be d (a positive integer) SUFFICIENT

2) d^(1/2)=x^2
square both sides
d=x^4
any number raised to an even root is a perfect square. square root of x^4 will always be an integer. SUFFICIENT
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Re: If d is a positive integer, is d^1/2 an integer? [#permalink]
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Re: If d is a positive integer, is d^1/2 an integer? [#permalink]
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