Square root (√) in LaTeX
\sqrt{x} produces a square root with a radical sign that stretches over its argument. An optional argument, \sqrt[n]{x}, sets the index for an nth root.
LaTeX command
\sqrt{x}Not the symbol you meant? Draw it to find the command →
Put the whole radicand in the braces so the bar covers it: \sqrt{x+1} spans x+1, whereas \sqrt x+1 only covers the x and leaves the +1 outside. The radical bar (vinculum) grows automatically to fit its contents, so \sqrt{x^2+y^2} and \sqrt{\frac{a}{b}} size themselves.
For an nth root use the optional argument in square brackets before the braces: \sqrt[3]{x} is a cube root and \sqrt[n]{x} the general case. This index sits in the crook of the radical sign.
A root can equally be written as a fractional exponent: \sqrt{x} equals x^{1/2}, and \sqrt[n]{x} equals x^{1/n}. Choose whichever reads more clearly in context. Very deeply nested roots can look cramped inline, so a displayed equation gives them room.
Other forms
\sqrt[3]{x}cube root / nth rootExamples
$\sqrt{2} \approx 1.414$a square root
$\sqrt{x^2 + y^2}$the bar stretches over the whole radicand
$\sqrt[3]{27} = 3$a cube root via the optional index
$\sqrt[n]{x} = x^{1/n}$the nth root as a fractional power
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$the quadratic formula
Tips and common mistakes
- Always brace the radicand:
\sqrt{x+1}covers x+1, whereas\sqrtx+1 covers only the x. - For an nth root use the optional argument:
\sqrt[3]{x} for a cube root,\sqrt[n]{x} generally. - The radical bar grows to fit, so
\sqrt{\frac{a}{b}}and\sqrt{x^2+y^2}size automatically. - A root can be written as a fractional exponent:
\sqrt{x}= x^{1/2}; use whichever is clearer. - Deeply nested roots look cramped inline; a displayed equation gives them room.
Working from handwritten notes?
LatexNotes turns a photo or PDF of handwritten mathematics into clean, compilable LaTeX - graphs and all. Free to try, no sign-up.
Convert your maths to LaTeX →FAQ
How do I write a square root in LaTeX?
Use \sqrt{x} in math mode, e.g. . Put the whole radicand in the braces so the bar covers it.
How do I write a cube root or nth root?
Use the optional index: \sqrt[3]{x} for a cube root and \sqrt[n]{x} for an nth root.
Why does my square root only cover the first symbol?
You omitted the braces. \sqrt x+1 renders as the root of x plus 1; write \sqrt{x+1} to place everything under the radical.
Can I write a root as a power instead?
Yes: \sqrt[n]{x} equals x^{1/n}, so is the same as . Use whichever reads more clearly.