Square Root in LaTeX

Write a square root with \sqrt{…}: \sqrt{x^2 + 1}. For a cube or nth root put the index in square brackets: \sqrt[3]{x}, \sqrt[n]{x}. The radical sign grows to fit whatever is inside the braces.

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Root commands

\sqrt{x}
$\sqrt{x}$
Square root.
\sqrt[3]{x}
$\sqrt[3]{x}$
Cube root.
\sqrt[n]{x}
$\sqrt[n]{x}$
nth root.
\sqrt{\frac{a}{b}}
$\sqrt{\frac{a}{b}}$
Root of a fraction; the sign stretches.
\sqrt{x^2 + y^2}
$\sqrt{x^{2} + y^{2}}$
Root over a longer expression.
x^{1/2}
$x^{1 / 2}$
Exponent form, when a radical would be too tall.
\sqrt[\leftroot{-2}\uproot{2} n]{x}
$\sqrt[n]{x}$
Moves the index (amsmath \leftroot, \uproot).
\surd
$\sqrt$
The √ sign alone, without a bar.

Try it live

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LaTeX

Templates

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Square root examples

Each result below is drawn from the LaTeX under it. Copy the code, edit it on this page, or open it in the full editor.

Quadratic formula
$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
LaTeX
```
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
```
Edit here Open in editor
Distance formula
$d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}$
LaTeX
```
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
```
Edit here Open in editor
Cube root
$\sqrt[3]{27} = 3$
LaTeX
```
\sqrt[3]{27} = 3
```
Edit here Open in editor
Nested radicals
$\sqrt{2 + \sqrt{2 + \sqrt{2}}}$
LaTeX
```
\sqrt{2 + \sqrt{2 + \sqrt{2}}}
```
Edit here Open in editor
Root of a fraction
$\sqrt{\frac{1 - \cos θ}{2}}$
LaTeX
```
\sqrt{\frac{1 - \cos \theta}{2}}
```
Edit here Open in editor
Even root heights
$\sqrt{a} + \sqrt{b} vs \sqrt{a} + \sqrt{b}$
LaTeX
```
\sqrt{a} + \sqrt{b} \quad \text{vs} \quad \sqrt{\vphantom{b} a} + \sqrt{b}
```
\vphantom{b} adds the height of a b without printing it, so both radicals line up.
Edit here Open in editor
Standard deviation
$σ = \sqrt{\frac{1}{N} \sum_{i = 1}^{N} (x_{i} - μ)^{2}}$
LaTeX
```
\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2}
```
Edit here Open in editor

How to write a root step by step

Use \sqrt in math mode and put everything under the radical in braces. Without braces only the next character goes under it: \sqrt x+1 means √x + 1.

For other roots add the index in square brackets before the braces: \sqrt[3]{x}. The index is set small in the notch of the radical.

Roots over letters of different heights come out uneven (√a is shorter than √b). Add a \vphantom or \mathstrut inside the lower one to match them.

Radical or exponent?

A radical over a tall fraction or a long sum becomes large and heavy. In those cases, and inside running text, (…)^{1/2} is easier to read and keeps the line height normal.

LaTeX

\[ \left( \frac{\sum_{i} x_i^2}{n} \right)^{1/2} \]

Common mistakes

Parentheses do not group in LaTeX. Only the “(” goes under the radical.
Instead of
```
\sqrt(x+1)
```
Write
```
\sqrt{x+1}
```
The index goes in square brackets. \sqrt{3}{x} is √3 followed by x.
Instead of
```
\sqrt{3}{x}  (meant as a cube root)
```
Write
```
\sqrt[3]{x}
```
A superscript on \sqrt is not an index; it raises a stray 3 after the radical sign.
Instead of
```
\sqrt^3{x}
```
Write
```
\sqrt[3]{x}
```

In Overleaf, MathJax and Word

Overleaf and pdfLaTeX
\sqrt and \sqrt[n] work in any document. \leftroot and \uproot for adjusting the index need \usepackage{amsmath}.
MathJax and KaTeX
MathJax and KaTeX support \sqrt, \sqrt[n] and \vphantom, so the same code works in Markdown, Jupyter and on web pages.
Microsoft Word
Word has radical templates, but pasted LaTeX is not converted reliably. Write the root here and use Copy for Word to paste an editable Word equation.

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