Tuesday, March 15, 2011

Get cube root of a number using PHP codes


In mathematics, a cube root of a number, denoted  or x1/3, is a number a such that a3 = x. All real numbers have exactly one real cube root and a pair of complex conjugate roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8 is 2, because 23 = 8. All the cube roots of −27i are
\sqrt[3]{-27i} = \begin{cases} \ \ \ \ \ \ \ \ \ \ \ 3i \\ \ \ \frac{3}{2}\sqrt3-\frac{3}{2}i \\ -\frac{3}{2}\sqrt3-\frac{3}{2}i. \end{cases} Display output :


The cube root operation is not associative or distributive with addition or subtraction.






The cube root operation is associative with exponentiation and distributive with multiplication and division if considering only real numbers, but not always if considering complex numbers, for example:
(\sqrt[3]{8})^3 = 8
but
\sqrt[3]{8^3} = \begin{cases} \ \ 8 \\ -4+4\sqrt{3}i \\ -4-4\sqrt{3}i. \end{cases}     Download the codes here

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