Cube root approximation is somewhat of a black art. Some implementations manipulate the exponent bits of the floating-point number; i.e. they arrive at an initial approximation by dividing the exponent by 3. Cubic equations, which are polynomial equations of the third degree (meaning the highest power of the unknown is 3) can always be solved for their three solutions in terms of cube roots and square roots (although simpler expressions only in terms of square roots exist for all three solutions, if at least one of them is a rational number). If two of the solutions are complex numbers, then all three
Nth root Any expression containing a radical, whether it is a square root, a cube root, or a higher root, is called a "radical expression", and if it contains no transcendental functions or transcendental numbers it is called an algebraic expression. In calculus, roots are treated as special cases of exponentiation, where the exponent is a fraction: Roots are particularly important in the theory of infinite series; the root test determines the radius of convergence of a power series. Roots can also be defined for complex numbers, and the complex roots of 1 (the roots of unity) play an important role in