Sure, let's go ahead and solve this problem.
We're given that the volume of the cube is 1,728 cubic inches.
The formula for the volume of a cube is found by taking the side length and cubing it: Volume = Side^3.
Where the '^' sign indicates raising to a power.
That means if we want to find the side length of the cube given its volume, we need to do the opposite operation. Since cubing is raising to the third power, the opposite operation is taking the cube root.
So to find the side length from the volume, we take the cube root of the volume: Side = CubeRoot(Volume).
So the side length is the cube root of 1,728 cubic inches.
Plug the value into the formula: Side = CubeRoot(1728), and we find the side length is approximately 11.999999999999998 inches.
For all intents and purposes, we can round this number to 12 inches, which is the exact cube root of 1,728.
So the side length of this cube is 12 inches.
This means each side of this cube measures 12 inches.
Answer: 12 inches.