Why can't we take a square root of a negative number?
Well, if you think at the meaning of the square root (inverse of the power of 2) you may find the answer.
this means that
(Actually, there are 2 numbers that give 4 when squared: 2 and -2)
You can not find a real number
You can not find, in the group of Real Numbers, a result of your negative square root...but you can try outside...in the group of immaginary numbers!!!!