Question

Cube roots of negative numbers exist in the set of real numbers, but square roots of negative numbers do not. Explain why this is true.

Answer 1

When problems with negatives under a square root first happened, mathematicians thought that there is no solution for the problem.

In an effort to answer this problem, mathematicians made a new number, i, which was denoted to as an "imaginary number", because it was not in the set of "Real Numbers".  The imaginary number "i" is √-1.

Answer 2

Cube roots of negative numbers exist in the set of real numbers, but square roots of negative numbers do not because it is not possible to get Square roots of negative real numbers because they do not exist in the real numbers. but they do exist in the complex numbers, It is not possible to square a value and arrive at a negative value.