nth root | root power
ArithmeticoperationInmathematics,annthrootofanumberxisanumberrwhich,whenraisedtothepowern,yields x:rn=x,{displaystyler{n}=x,}wherenisapositiveinteger,sometimescalledthedegreeoftheroot.Arootofdegree2iscalledasquarerootandarootofdegree3,acuberoot.Rootsofhigherdegreearereferredbyusingordinalnumbers,asinfourthroot,twentiethroot,etc.Thecomputationofannthrootisarootextraction.Forexample,3isasquarerootof9,since32=9,and−3isalsoasquarerootof9,since(−3)2=9.Anynon-zeronumberconsideredasacomplexnumberha...
Arithmetic operation
In mathematics, an nth root of a number x is a number r which, when raised to the power n, yields x:
rn=x,{displaystyle r{n}=x,}where n is a positive integer, sometimes called the degree of the root. A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree are referred by using ordinal numbers, as in fourth root, twentieth root, etc. The computation of an nth root is a root extraction.
For example, 3 is a square root of 9, since 32 = 9, and −3 is also a square root of 9, since (−3)2 = 9.
Any non-zero number considered as a complex number has n different complex nth roots, including the real ones (at most two). The nth root of 0 is zero for all positive integers n, since 0n = 0. In particular, if n is even and x is a positive real number, one of its nth roots is real and positive, one is negative, and the others (when n > 2) are non-real complex numbers; if n is even and x is a nega...