A factory makes cardboard boxes in the shape of cubes. Given V, the volume of a box in cubic inches, which of the following describes the boxes that have edge lengths which are rational numbers?
A.
V is a number that cannot be a perfect cube but can be a decimal number with a rational cube root.
B.
V is a number that is neither a perfect cube nor a decimal number with a rational cube root.
C.
V is a number that is a perfect cube but not a decimal number with a rational cube root.
D.
V is a number that is either a perfect cube or a decimal number with a rational cube root.
To have edge lengths which are rational numbers, the volume must be a perfect cube. This means that the volume has to be a number that is a perfect cube but not a decimal number with a rational cube root.
Answer: C.