Data Sufficiency

Here is the question:

Is "n" an integer?

(1) n^2 is an Integer.
(2) The square root of n is an integer

The answer is "B" and I understand that (2) is sufficient, but I do not understand why (1) is not also sufficient. If n^2 is an integer, doesn't "n" have to be an integer? I can't think of any non-integers that would satisfy this.

Any explanations would be greatly appreciated!

Take for example sqrt(2).

sqrt(2) * sqrt(2) is an integer 2 but sqrt(2) itself is not an integer