8th Class Chapter No 7 - Cubes & Cube Roots in Maths for CBSE NCERT
In mathematics, a cube root of a number x is a number y such that y3 = x. All real numbers (except zero) 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 3√8, is 2, because 23 = 8, while the other cube roots of 8 are −1 + √3i and −1 − √3i. The three cube roots of −27i are {displaystyle 3i,quad {frac {3{sqrt {3}}}{2}}-{frac {3}{2}}i,quad { ext{and}}quad -{frac {3{sqrt {3}}}{2}}-{frac {3}{2}}i.} 3i,quad {frac {3{sqrt {3}}}{2}}-{frac {3}{2}}i,quad { ext{and}}quad -{frac {3{sqrt {3}}}{2}}-{frac {3}{2}}i. The cube root operation is not associative or distributive with addition or subtraction. 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√. 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, the cube of any cube root of 8 is 8, but the three cube roots of 83 are 8, −4 + 4i√3, and −4 − 4i√3.
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