Question

Explain why the square root of -4 is not a real number, but cube root of -8 is

Answer 1

Because -2 times -2 is 4 and 2 x 2 is 4 as well. So you cant have -4. 
But if you have cube root of -8, you can do -2 as -2 x -2 gives you 4, if you x this by -2 you get -8