Question

Why can't we take a square root of a negative number?

Answer 1

Well, if you think at the meaning of the square root (inverse of the power of 2) you may find the answer.
Consider: `sqrt4=a`
this means that `a` must be a number such that: `a^2=4`
(Actually, there are 2 numbers that give 4 when squared: 2 and -2)
Now consider `sqrt(-4)=b`
You can not find a real number `b` that squared gives you -4!!!

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!!!!