This is slightly misleading - strength actually changes as the square of the dimension or the cube of the dimension, depending on which strength you're talking

This is slightly misleading - strength actually changes as the square of the dimension or the cube of the dimension, depending on which strength you're talking about. Axial (tension, compression) and shear strength are derived from net area and so scale with by x^2. Flexural strength is derived from a factored second moment of inertia which happens to work out to x^3.