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

We can't take a square root of a negative number because whenever you multiply any number by itself, whether it is positive or negative, you will always get a positive number.

e.g.
2 * 2 = +4
(-3) * (-3) = +9

So if you try to take a square root of a negative number, you will come to a problem as there are not any number when you multiply it by itself you will get a negative answer.
Because of that we invented imaginary numbers where i = sqrt(-1) so we could factor out the negative and continue on with our work.