Question

Explain why the square root of -64 is undefined but the cubed root of -64 is defined in the real number system

Answer 1

Because there is no number that could be multiplied BY ITSELF and still be negative:
-2 x -2 = 4
2 x 2 = 4
But, cubed root works because a negative can be three times and still be negative:
-4 x -4 x -4 = -64
Hope this helps!