Square Root Symbol (√)

What Does the Square Root Symbol Mean?

Quick answer: The square root symbol (√) asks “what number, multiplied by itself, gives this number?” For example, √9 = 3, because 3 × 3 = 9. It’s also called the radical sign or root symbol, and by convention it always refers to the non-negative (“principal”) root.

The square root symbol (√) represents the square root operation: it asks what number, multiplied by itself, produces the number underneath it. √16 = 4, because 4 × 4 = 16.

The number under the symbol is called the radicand. The whole expression — symbol plus radicand — is sometimes called a radical. The horizontal line that extends over the radicand is the vinculum; it groups everything underneath as a single unit, the same way parentheses do.

You’ll see the square root symbol called by several different names depending on the textbook, country, or context:

• Radical sign / radical symbol
• Root symbol or root sign
• Sqrt symbol
• Surd (more common in British English, technically refers to an irrational root)
• Radix sign (from the Latin word the symbol is believed to come from)

All of these point at the same character. There’s no meaningful difference between “square root symbol” and “radical sign” — they’re interchangeable in everyday use.

One technical note worth knowing: the plain Unicode character √ doesn’t actually include the connecting overline that printed math books show stretching over multi-digit numbers. That overline (the vinculum) is added separately by typesetting systems like LaTeX. If you copy-paste √ into a plain text document and it looks slightly “incomplete” compared to a textbook, that’s why — it’s working correctly, it just isn’t carrying its overline with it.

√ vs ∛ vs ∜ vs the Radical Sign vs a Checkmark

These characters get mixed up constantly, and the confusion is legitimate — they really do look similar at small sizes.

The square root symbol is the only one of these that doesn’t need a small number written above it — it’s understood to mean “2nd root” by default. The cube and fourth root symbols always carry their index (the small 3 or 4) to show which root they mean. The checkmark is visually close to a bare radical sign but has nothing to do with mathematics.

For higher roots — 5th, 6th, and beyond — there’s no dedicated Unicode character. Mathematicians write a small index number above a generic radical sign instead: ⁵√32 means “the 5th root of 32.”

Is the Square Root Symbol Always Positive?

Yes. By mathematical convention, √ always refers to the non-negative root — what mathematicians call the principal square root. √9 is 3, not −3, even though both 3 and −3 satisfy 3² = 9 and (−3)² = 9.

There’s a real difference between two related questions that look almost identical:

• “What is √9?” has one answer: 3. The radical symbol is defined to give only the positive root.
• “What are the solutions to x² = 9?” has two answers: x = 3 or x = −3. Squaring throws away the sign, so solving the equation has to bring both possibilities back — which is why the quadratic formula carries a ± in front of the radical, while a plain √ never does.

This is a deliberate, centuries-old convention that exists so √ can behave as a proper mathematical function — one input, one output — rather than an ambiguous operation. Read the full explainer, including where Bhāskara II, Christoph Rudolff, and Augustin-Louis Cauchy fit into the story →

How to Type the Square Root Symbol

There’s no dedicated √ key on any standard keyboard, so every method below works around that in a different way. Pick whichever matches your device.

On Windows

Hold Alt and type 251 on the numeric keypad (NumLock must be on), then release Alt. If you don’t have a numeric keypad, open the Windows Character Map (search “charmap”), find √ under Mathematical Operators, and copy it from there.

On Mac

Press Option + V. That’s the entire shortcut — no modifier combinations, no numeric codes. Full Mac guide →

On Chromebook and Linux

Press Ctrl + Shift + U, type 221a (the Unicode hex code), then press Enter or Space. This works system-wide on ChromeOS and most Linux distributions. Full Chromebook guide →

On iPhone and Android

Neither mobile keyboard has a built-in square root key. Your two practical options: copy and paste the symbol from the top of this page, or set up a text-replacement shortcut (iPhone: Settings → General → Keyboard → Text Replacement).

How to Insert √ in Word, Excel, Google Docs, and LaTeX

Microsoft Word

Use Insert → Symbol → More Symbols, select Mathematical Operators, and double-click √. Or type 221A and immediately press Alt + X to auto-convert it.

Microsoft Excel

To calculate a square root, use =SQRT(number). To insert the character itself, use =UNICHAR(8730) or Insert → Symbol.

Google Docs

Go to Insert → Special characters, then search “square root” or “radical.”

LaTeX

\sqrt{x} produces a square root with the vinculum included. \sqrt[n]{x} produces an nth root. \surd produces the bare radical symbol with no vinculum and no radicand.

Python and Other Code

math.sqrt(x) returns the square root as a float. x ** 0.5 does the same with no import required. math.isqrt(x) returns the integer (floor) square root.

Unicode, HTML, and Code Values

Where Does the Square Root Symbol Come From?

The radical sign has been evolving for roughly 500 years. German mathematician Christoff Rudolff is credited with the first printed use of √ — without the connecting overline — in his 1525 book Die Coss. Over a century later, René Descartes united that radical sign with the vinculum in his 1637 work La Géométrie, producing the symbol recognizable today.

The word “radical” traces to the Latin radix, meaning “root.” There’s a competing theory that the symbol’s shape descends from the Arabic letter ج (jīm), the first letter of jadhr (root); Leonhard Euler instead believed it came from a stylized Latin “r.” Neither theory is fully settled.

Read the full history, including the legacy encoding tables and the principal-root debate →

Where You’ll Actually See the Square Root Symbol

Outside of homework, the radical sign shows up constantly across math, science, and engineering:

• Pythagorean theorem: the hypotenuse of a right triangle is c = √(a² + b²)
• Quadratic formula: x = (−b ± √(b² − 4ac)) / 2a
• Standard deviation in statistics: σ = √(variance)
• Distance formula: √((x₂−x₁)² + (y₂−y₁)²)

In every one of these, the symbol means exactly the same thing it means on its own: take the non-negative square root of whatever’s underneath the bar.