HELP PLEASE :(

Three-Dimensional Geometry
Geometric Design
1. Kathrine, Giana, and Jackson are designing jewelry boxes to sell at the art fair. The
dimensions of their boxes are:
Kathrine: 5in x 5in x 5in
Giana: 10in X 12in X 2in
Jackson: 10in X 5in x 4in
If a customer at the art fair is wants to buy the jewelry box that will hold the most amount
of jewelry, whose jewelry box should they purchase?

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?