Square Root in LaTeX (\sqrt{x})

Where it is used

Draws a radical sign over its argument, giving the principal square root of x.

\sqrt automatically stretches the radical to cover whatever you put in braces, so \sqrt{x^2 + y^2} gets a longer vinculum and a taller sign. It is the standard way to write the Euclidean norm, the quadratic formula, and standard deviation as \sqrt{\operatorname{Var}(X)}. Radicals over arguments with different heights can look uneven; adding \vphantom{y} or \mathstrut inside makes neighboring roots match. For an index such as a cube root, use the optional argument \sqrt[3]{x}. In inline text, x^{1/2} is sometimes clearer than a radical over a tall fraction.

Minimal compilable example

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

\documentclass{article}
\begin{document}
Square Root: $\sqrt{x}$

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
\end{document}

Related symbols

• N-th Root\sqrt[n]{x}
• Fraction\frac{a}{b}
• Summation\sum_{i=1}^{n}
• Division\div
• Product\prod_{i=1}^{n}
• Multiplication\times

Frequently asked questions

How do I write Square Root in LaTeX?

Type \sqrt{x} in math mode, for example $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. It works in plain LaTeX without loading any package.

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

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

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

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