Do you know what you are finding when you take the square root of a number? Most students don't have a clue. When you take the square root you are finding the side length of a square with a given area. It is not just some random button we push on the calculator to get huge messy irrational numbers on the screen. The square root function is a geometric problem.
Cubes on the right.
So, what are we finding when we take the cube root of a number? Well, the answer shouldn't surprise you. We are finding the side length of a cube with a given volume.