A company sells various sizes of jewelry boxes that are in the shape of a cube. Which volume of cubes has a rational number of side lengths
1.5 feet ^3
3 yards ^3
8 inches ^3
33 centimeters ^3
1.5 feet ^3 has a rational number of side lengths because it can be represented as 1.5 = (3/2) feet, which is a rational number.
8 inches ^3 has a rational number of side lengths because it can be represented as 2 inches, which is a rational number.
33 centimeters ^3 has a rational number of side lengths because it can be simplified to (11/3) centimeters, which is a rational number.
However, 3 yards ^3 does not have a rational number of side lengths. This is because 3 yards is equal to 9 feet, but the cube has a volume measured in cubic yards. To convert to cubic yards, we need to divide by 27 (since 1 cubic yard is equal to 27 cubic feet). So, 3 yards ^3 is equal to (9/27) yards ^3 which simplifies to 1/3 yards ^3, hence the side lengths are irrational.