can you square root a negative number.

Yes you can, I would think..

Let's try a few to see if we can...

sqrt(-1)=1i   That one we can't...

sqrt(-2) = 1.414213562373095i        We sort of can there...

sqrt(-4) = 2i    I am not sure about that one.

I've concluded that any square root of a negative number would be the normal square root times i.

Yes, you can but the result/answer is an imaginary number with 'i' in it.  'i' is defined as the sqrt(-1).

example:   sqrt(-9) = sqrt (-1 x 9) =  3sqrt(-1)  = 3i

sqrt(-5) = sqrt(-1 x 5) = 2.236i