---
tag: TTEA3KA5KJ
kind: concept
name: Nth root
aliases: [3-root, eighth-root, eleventh-root, fifth-root, fourth-root, n-th-root, n-th-root-algorithm, ninth-root, nth-root-algorithm, nth-root-extraction, nth-roots, principal-root, properties-of-radicals, radical-expression, radical-root, radical-signs, radicand, radication, root-extraction, seventh-root, sixth-root, surd-mathematics, surds-and-indices, tenth-root, twelfth-root]
sources:
  - wikipedia: en:235029@r1376319850
    locator: Nth root
    note: adopted
    mention: wikipedia://en/235029
    sections: [Summary]
same_as:
  wikidata: Q601053
  wikipedia: Nth root
inventory: [FK8QVG00Y4]
---

## Summary

In mathematics, an **$n$th root** of a number $x$ is the number $r$ which, when $n$ copies are multiplied together, yields $x$:

$$r^n = \underbrace{r \times r \times \dotsb \times r}_{n\text{ factors}} = x.$$

The positive integer $n$ is called the *index* or *degree*, and the number $x$ of which the root is taken is the *radicand.* A root of degree 2 is called a *[[square root|0F7FQS6XY6]]* 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 $n$th root is a **root extraction**.