If you want to check whether a cube root is correct, simply cube your solution and see if you get back the number under the radical. In this case, we can check that [tex] \sqrt[3]{-512} =-8 [/tex] by cubing -8, getting us
[tex] (-8)^3=(-8)\cdot(-8)\cdot(-8)=64\cdot(-8)=-512 [/tex]
Our check checks out!
