In mathematics, an nth root of a number x is a number r which, when raised to the power of n, yields x: r n = r × r × ⋯ × r ⏟ n  factors = x . {\displaystyle...

every nonzero element of a finite field is a root of unity. Any algebraically closed field contains exactly n nth roots of unity, except when n is a multiple...

depicted above. Apotome (mathematics) Cube root Functional square root Integer square root Nested radical Nth root Root of unity Solving quadratic equations...

nth root for positive real radicands. For negative real radicands, and odd exponents, the principal nth root is not real, although the usual nth root...

of a number x is written as x , {\displaystyle {\sqrt {x}},} while the nth root of x is written as x n . {\displaystyle {\sqrt[{n}]{x}}.} It is also used...

root of numbers having many digits in the Aryabhatiya (section 2.5). Methods of computing square roots List of polynomial topics Nth root Square root...

The two inverses of tetration are called super-root and super-logarithm, analogous to the nth root and the logarithmic functions. None of the three...

an integer, and let α ∈ R {\displaystyle \alpha \in R} be a principal nth root of unity, defined by: The discrete Fourier transform maps an n-tuple (...

defined to be the root with the non-negative real part. Alpha max plus beta min algorithm nth root algorithm Fast inverse square root The factors two and...

In mathematics, a primitive root may mean: Primitive root modulo n in modular arithmetic Primitive nth root of unity amongst the solutions of zn = 1 in...

{p}}}} is well-defined and congruent to a unique nth root of unity ζns. This root of unity is called the nth-power residue symbol for O k , {\displaystyle...

composition. Commonly, the basic functions that are allowed in closed forms are nth root, exponential function, logarithm, and trigonometric functions. However...

{\sqrt[{n}]{x}}^{n}} by x (this is allowed, as, by definition, a nth root of x is a number that has x as its nth power). If k ≥ n, one writes k = qn + r with 0 ≤ r...

programs nth root of a number Root of unity, a complex number which is an nth root of one Root of an equation, a solution of the equation Root of a function...

obtained by a tower of field extensions, each generated by adjoining an nth root of an element from the previous field. A simple radical extension is a...

Number of times an object must be counted for making true a general formula nth root algorithm System of polynomial equations – Roots of multiple multivariate...

their sum). The geometric mean of ⁠ n {\displaystyle n} ⁠ numbers is the nth root of their product, i.e., for a collection of numbers a1, a2, ..., an, the...

and PSL(n, F) are isomorphic if and only if every element of F has an nth root in F. As an example, note that PGL(2, C) = PSL(2, C), but that PGL(2, R)...

{\text{power}}} nth root (√) radicand degree = {\displaystyle \scriptstyle {\sqrt[{\text{degree}}]{\scriptstyle {\text{radicand}}}}\,=\,} root {\displaystyle...

number has two square roots, three cube roots, and in general n nth roots. The only nth root of 0 is 0. The complex logarithm function is multiple-valued...

contains a primitive nth root of unity, then it is a radical extension and the elements of L can then be expressed using the nth root of some element of...

contains n distinct nth roots of unity, which implies that the characteristic of K doesn't divide n, then adjoining to K the nth root of any element a of...

rational numbers of any primitive nth-root of unity ( e 2 i π / n {\displaystyle e^{2i\pi /n}} is an example of such a root). An important relation linking...

field which is the product of numbers of the form (ζa n − 1) for ζ n an nth root of unity and 0 < a < n. The cyclotomic units form a subgroup of finite...

complex nth root of a complex number. (This is in contrast to the roots of a positive real number x, which has a unique positive real n-th root, which...

K be a field in which n is invertible such that K contains a primitive nth root of unity ζ. For nonzero elements a and b of K, the associated cyclic algebra...

the operations of addition, subtraction, multiplication, division, and nth root extraction. The Abel–Ruffini theorem proves that this is impossible. However...

converge absolutely, conditionally or diverge. This is also known as the nth root test or Cauchy's criterion. Let r = lim sup n → ∞ | a n | n , {\displaystyle...

\det(A+B)\geq \det(A)+\det(B){\text{.}}} Brunn–Minkowski theorem implies that the nth root of determinant is a concave function, when restricted to Hermitian positive-definite...

that is, extensions generated by adjoining an nth root to a field already containing a primitive nth root of unity. This is a significant extension of...