On number 3 plz explain to me i don't understand this because problem

The volume of a cube is 8 in to the 3rd power. how long is each side?

Ineed in figuring out this problem.

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?