If the square root of p^2 is an integer, which of the following must be true?
I. p^2 has an odd number of factors
II. p^2 can be expressed as the product of an even number of prime factors
III. p has an even number of factors	Pick one:
A) I B) II C) III D) I and II E) II and III
I. p^2 is a perfect square and a perfect square has pairs of factors and '1' with it. The total number of factors is odd   II. If p = 3 then p^2 = 9. The prime factors will always remain even as the p is an integer and the pairs have to come out of square root to make p an integer.   III. This is not true always. Let us say p = 4, it has three factors: 1, 2 and 4. Hence it will not hold true always.   Hence I and II is the answer.
<result>D</result>
If the square root of p^2 is an integer, which of the following must be true?
I. p^2 has an odd number of factors
II. p^2 can be expressed as the product of an even number of prime factors
III. p has an even number of factors