Because it was discovered by Jaques Cube when he was using his calculator while walking and he tripped over a root and accidentally hit the square root key, then a number, then ^ carrot key, then hit 1 divided by 3 then enter while he was falling
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The non-idiotic answer is that the volume of a cube is a side times a side times a side (a side cubed). Calculating the cube root is the inverse function of cubing, the root being the basic part you started with, a side.
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The cube root is the side of a cube.
4
cube root (pi) = 1.46459189.
The cube root of 0.027 is 0.30000000000000004
The cube root of 480 = 7.829735