Obviously 1 ≠ -1, so both conclusions cannot be true.
The short answer is that √(ab) = √a √b is always true if a and b are both non-negative integers, but not always true otherwise. The case here is one in which the identity does not apply. "√a" literally means "the positive number such that its square is a". But you're using the convention that √(-1) = i, and i is not a positive number, so this identity does not apply.
The correct result is i ² = -1.
That's not to say that the identity above is always wrong whenever a or b are not non-negative. For example,
√(-25) = √((-1) × 5²) = √(-1) × √(5²) = 5i
