cube root
cube root
English Definitions:
cube root (noun)
a number that when multiplied three times equals a given number
cube root (Noun)
Of a number or expression, a number or expression the cube of which is equal to the given number or expression.
Cube root
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 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: but
Cube root
In mathematics, a cube root of a number x is a number y such that y3 = 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 8 3 {\displaystyle {\sqrt[{3}]{8}}} , is 2, because 23 = 8, while the other cube roots of 8 are − 1 + i 3 {\displaystyle -1+i{\sqrt {3}}} and − 1 − i 3 {\displaystyle -1-i{\sqrt {3}}} . The three cube roots of −27i are 3 i , 3 3 2 − 3 2 i , and − 3 3 2 − 3 2 i . {\displaystyle 3i,\quad {\frac {3{\sqrt {3}}}{2}}-{\frac {3}{2}}i,\quad {\text{and}}\quad -{\frac {3{\sqrt {3}}}{2}}-{\frac {3}{2}}i.} In some contexts, particularly when the number whose cube root is to be taken is a real number, one of the cube roots (in this particular case the real one) is referred to as the principal cube root, denoted with the radical sign 3 . {\displaystyle {\sqrt[{3}]{~^{~}}}.} The cube root is the inverse function of the cube function if considering only real numbers, but not if considering also complex numbers: although one has always ( x 3 ) 3 = x , {\displaystyle \left({\sqrt[{3}]{x}}\right)^{3}=x,} the cube of a nonzero number has more than one complex cube root and its principal cube root may not be the number that was cubed. For example, ( − 1 + i 3 ) 3 = 8 {\displaystyle (-1+i{\sqrt {3}})^{3}=8} , but 8 3 = 2. {\displaystyle {\sqrt[{3}]{8}}=2.}
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"cube root." Kamus.net. STANDS4 LLC, 2024. Web. 26 Apr. 2024. <https://www.kamus.net/english/cube+root>.
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