Doubling the cube For instance, we cannot construct the number , since this number has degree 3, because it is a root of the irreducible polynomial x3 − 2. This fact is pertinent for the confounding classical problem known as doubling the cube. The problem is, given a side length AB of a cube, to construct a side length CD for a cube of twice the volume. If one regards the original length AB as a unit length, then the first cube will have volume 1, and so the doubled cube will have volume 2, and consequently, side length . Ultimately, therefore, the problem of doubling the cube is exactly the
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