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nthroot
nth root
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There are 7 letters in NTHROOT ( H4N1O1R1T1 )
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Definitions of nth root in various dictionaries:
NTH ROOT - In mathematics, an nth root of a number x, where n is usually assumed to be a positive integer, is a number r which, when raised to the power n yield...
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Nth root description |
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In mathematics, an nth root of a number x, where n is usually assumed to be a positive integer, is a number r which, when raised to the power n yields x:* * * * * r * * n * * * = * x * , * * * {\displaystyle r^{n}=x,} * where n is 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. * For example: * * 3 is a square root of 9, since 32 = 9. * −3 is also a square root of 9, since (−3)2 = 9.Any non-zero number, considered as complex number, has n different "complex roots of degree n" (nth roots), including those with zero imaginary part, i.e. any real roots. The root of 0 is zero for all degrees n, since 0n = 0. In particular, if n is even and x is a positive real number, one of its nth roots is positive, one is negative, and the rest (when n > 2) are complex but not real; if n is even and x is a negative real, none of the nth roots is real. If n is odd and x is real, one nth root is real and has the same sign as x, while the other (n − 1) roots are not real. Finally, if x is not real, then none of its nth roots is real. * Roots are usually written using the radical symbol or radix with * * * * * * x * * * * * {\displaystyle {\sqrt {x}}} * denoting the principal square root of * * * * x * * * {\displaystyle x} * , * * * * * * x * * 3 * * * * * * {\displaystyle {\sqrt[{3}]{x}}} * denoting the principal cube root, * * * * * * x * * 4 * * * * * * {\displaystyle {\sqrt[{4}]{x}}} * denoting the principal fourth root, and so on. In the expression * * * * * * x * * n * * * * * * {\displaystyle {\sqrt[{n}]{x}}} * , n is called the index, * * * * * * * * * * * {\displaystyle {\sqrt {\;}}} * is the radical sign or radix, and * * * * x * * * {\displaystyle x} * is called the radicand. Since the radical symbol denotes a function, it is defined to return only one result for a given argument * * * * x * * * {\displaystyle x} * , which is called the principal nth root of * * * * x * * * {\displaystyle x} * . Conventionally, a real root, preferably non-negative, if there is one, is designated as the principal nth root. * A complementary definition of principal root (though not formally defined or universally accepted) is to say that it is always the complex root that has the least value of the argument amon... |