Why is it a problem to find the square root of a negative number, for example √-4?

It is not possible because no number times itself can equal a negative number.

Taking the square root of a negative number is a problem because this technically does not follow the rules of a square root. A square root is made of a number times itself, and therefore, is impossible to have a negative times a positive to make a negative total (An example would be √4, as the answer can be 2 (because 2 x 2 = 4) or -2 (because -2 x -2 = 4)).

This means that in order to solve √-4, you must use imaginary numbers. This is represented by "i."

For the example of √-4, your answer would be 2i. These imaginary numbers are used whenever you are square rooting a negative number in order to show that it is breaking the real rules of roots.