Every complex number other than 0 has n different nth roots.

This formula can be used to find nth root of a complex number.

Problems can occur when taking the nth roots of negative or complex numbers.

The nth root can also be represented using exponentiation as x.

Thus finding nth roots in the complex plane can be segmented into two steps.

This is also known as the nth root test or Cauchy's criterion.

Furthermore, all n of the nth roots are at equally spaced angles from each other.

Each complex number has three cube roots or, in general, n nth roots.

The nth root of a number; specific examples include:

The number n divides q-1 because the local field contains the nth roots of unity by assumption.

Every positive real number x has a single positive nth root, which is written .

For odd values of n, every negative number x has a real negative nth root.

There is a very fast-converging nth root algorithm for finding :

Also useful is this generalized continued fraction, based on the nth root method:

Similarly, if the exponent is the result is the nth root, so:

Thus y is the largest integer less than the nth root of x, and r is the remainder.

The geometric mean of n non-negative numbers is obtained by multiplying them all together and then taking the nth root.

Geometric mean - the nth root of the product of the data values, where there are n of these.

For the Galois group of a polynomial, these cyclic groups correspond to nth roots (radicals) over some field.

Every positive real number has a positive nth root and the rules for operations with such surds are straightforward:

All nth roots of integers, or in fact of any algebraic number, are algebraic.

That is, a measure is infinitely divisible if it is possible to define all nth roots.

It may be seen that this process uses a generalization of the nth root, which may be expressed as:

Recall that an nth root can be rewritten in exponential format, so that is equivalent to .

The number of alternatives are equivalent to the root or nth root of a mathematical or logical variable.