N-th Root in LaTeX (\sqrt[n]{x})

Where it is used

Writes the n-th root of x, with the index n placed in the crook of the radical sign.

The index goes in square brackets before the radicand, so \sqrt[3]{8} = 2 is a cube root and \sqrt[n]{x} denotes x^{1/n}. It shows up in the root test for series, \limsup \sqrt[n]{|a_n|}, and in geometric means \sqrt[n]{x_1 x_2 \cdots x_n}. TeX sometimes places the index awkwardly, especially for tall indices; \leftroot{} and \uproot{} nudge it, as in \sqrt[\leftroot{-2}\uproot{2}n]{x}. Keep the index short: for complicated exponents, writing the power x^{1/(k+1)} is easier to read than a radical.

Minimal compilable example

Paste this into an empty .tex file and compile it with pdfLaTeX, XeLaTeX or LuaLaTeX.

\documentclass{article}
\begin{document}
N-th Root: $\sqrt[n]{x}$

\[ \sqrt[n]{x_1 x_2 \cdots x_n} \le \frac{x_1 + \cdots + x_n}{n} \]
\end{document}

Related symbols

• Summation\sum_{i=1}^{n}
• Square Root\sqrt{x}
• Product\prod_{i=1}^{n}
• Fraction\frac{a}{b}
• Integral\int_{a}^{b}
• Division\div

Frequently asked questions

How do I write N-th Root in LaTeX?

Type \sqrt[n]{x} in math mode, for example $\sqrt[n]{x_1 x_2 \cdots x_n} \le \frac{x_1 + \cdots + x_n}{n}$. It works in plain LaTeX without loading any package.

Which package do I need for \sqrt[n]{x}?

None. \sqrt[n]{x} is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use \sqrt[n]{x} in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\sqrt[n]{x}$ in running text.