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;
Square root of 5 of a side located on one the faces containing that vertex and opposite to it, are in the ratio This follows from the geometrical relationships between a cube and the quantities (edge-to-face-diagonal ratio, or distance between opposite edges), (edge-to-cube-diagonal ratio) and (the relationship just mentioned above). A rectangle with side proportions 1: is called a "root-five rectangle" and is part of the series of root rectangles, a subset of dynamic rectangles, which are based on and successively constructed using the diagonal of the previous root rectangle, starting from a square. A root-5 rectangle is particularly notable in that it can