: Mathematics: cube root

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cube root

In mathematics, a cube root of a number $x$ is a number $y$ such that $y 3 = x$ . All nonzero real numbers have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of $8$ , denoted ${\\displaystyle {\\sqrt[{3}]{8}}}$ , is $2$ , because $23 = 8$ , while the other cube roots of $8$ are ${\\displaystyle -1+i{\\sqrt {3}}}$ and ${\\displaystyle -1-i{\\sqrt {3}}}$ . The three cube roots of $-27 i$ are:
${\\displaystyle 3i,\\quad {\ rac {3{\\sqrt {3}}}{2}}-{\ rac {3}{2}}i,\\quad {\ ext{and}}\\quad -{\ rac {3{\\sqrt {3}}}{2}}-{\ rac {3}{2}}i.}$