Cube root solution expressions involve the real cube root of a real number, while if all three solutions are real numbers then they may be expressed in terms of the complex cube root of a complex number. Quartic equations can also be solved in terms of cube roots and square roots. The calculation of cube roots can be to traced back to Babylonian mathematicians from as early as 1800 BCE. In the fourth century BCE Plato posed the problem of doubling the cube, which required a compass-and-straightedge construction of the edge of a cube with twice the volume of a given cube;
Doubling the cube at solving what they saw as an obstinate but soluble problem. However, the nonexistence of a solution was finally proven by Pierre Wantzel in 1837. In algebraic terms, doubling a unit cube requires the construction of a line segment of length , where ; in other words, . This is because a cube of side length 1 has a volume of , and a cube of twice that volume (a volume of 2) has a side length of the cube root of 2. The impossibility of doubling the cube is therefore equivalent to the statement that is not a constructible