Cube Root

$\begin{figure}\begin{center}\BoxedEPSF{CubeRoot.epsf}\end{center}\end{figure}$

$\begin{figure}\begin{center}\BoxedEPSF{CubeRootReIm.epsf scaled 660}\end{center}\end{figure}$

Given a number , the cube root of , denoted $\root 3\of z$ or $z^{1/3}$ ( to the 1/3 Power), is a number such that . There are three (not necessarily distinct) cube roots for any number.

$\begin{figure}\begin{center}\BoxedEPSF{CubeRootDerivative.epsf scaled 900}\end{center}\end{figure}$

For real arguments, the cube root is an Increasing Function, although the usual derivative test cannot be used to establish this fact at the Origin since the derivative approaches infinity there (as illustrated above).