Final answer:
To find the side length of the cube, we take the cube root of the volume. The number 200 is neither a perfect square nor a perfect cube.
Step-by-step explanation:
To find the length of each side of the cube, we need to find the cube root of the volume. So, the cube root of 512 cubic inches is 8 inches. Therefore, each side of the cube is 8 inches long.
Regarding the number 200, it is neither a perfect square nor a perfect cube. A perfect square is a number that can be expressed as the square of an integer, while a perfect cube is a number that can be expressed as the cube of an integer. Since the square root of 200 is not an integer and the cube root of 200 is not an integer, 200 is neither a perfect square nor a perfect cube.
Learn more about Calculating length of a cube, perfect squares and cubes