How do you compute the diagonal of a cube?

If each cube side is of length s, then the diagonal of the BASE is from Pythagorean theorem

sqrt ( s^2 + s^2) = sqrt (2) times s = 1.414s

The height of the cube is s, so we use the theorem again using the base diagonal and height to get the cube diagonal:

sqrt( (1.414s)^2 + s^2) = sqrt (3s^2) = sqrt(3) times s = 1.732s