# Definitions for **nth root**

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nth root

In mathematics, the nth root of a number x is a number r which, when raised to the power of n, equals 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 to using ordinal numbers, as in fourth root, twentieth root, etc. For example: ⁕2 is a square root of 4, since 2² = 4. ⁕−2 is also a square root of 4, since ² = 4. A real number or complex number has n roots of degree n. While the roots of 0 are not distinct, the n nth roots of any other real or complex number are all distinct. If n is even and the radicand is real and positive, one of its nth roots is positive, one is negative, and the rest are complex but not real; if n is even and the radicand is real and negative, none of the nth roots is real. If n is odd and the radicand is real, one nth root is real and has the same sign as the radicand, while the other roots are not real. Roots are usually written using the radical symbol or radix or, with or denoting the square root, denoting the cube root, denoting the fourth root, and so on. In the expression, n is called the index, is the radical sign or radix, and x is called the radicand. When a number is presented under the radical symbol, it must return only one result like a function, so a non-negative real root, called the principal nth root, is preferred rather than others. An unresolved root, especially one using the radical symbol, is often referred to as a surd or a radical. Any expression containing a radical, whether it is a square root, a cube root, or a higher root, is called a radical expression.

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