The square root symbol (√)
The square root symbol √ asks a question backwards: which number, multiplied by itself, gives the one under the bar? This page copies the radical family — square, cube and fourth roots — with worked examples, the typing routes for each platform, and the story of a sign that began life as a handwritten letter r.
Copy the root symbols
Worked examples to copy
Reading the radical family
| Sign | Name | Code | What it asks |
|---|---|---|---|
| √ | Square root | U+221A | x × x = the radicand — √25 = 5 |
| ∛ | Cube root | U+221B | x × x × x = the radicand — ∛27 = 3 |
| ∜ | Fourth root | U+221C | x⁴ = the radicand — ∜81 = 3 |
The little number tucked into the crook (the 3 in ∛) is the index; square roots omit it because 2 is the default. The bar over the contents — the vinculum — is the sign’s second half: it groups everything beneath it, which is why √(a + b) and √a + b are different statements. In computing, the same operation wears a name instead of a sign: the sqrt symbol becomes the sqrt() function — SQRT in Excel and Sheets, sqrt in Python and most code.
The “under root” way of saying it
In Indian and Pakistani classrooms this mathematical root symbol is often read aloud by its shape: a number is “under root” — “under root 2” for √2, “under root 5” for √5. The phrase describes the picture exactly (the number sits under the radical’s bar), and the under root symbol it names is the same √ used everywhere else; British classrooms saying the maths root symbol and American ones saying “square root of” are all pointing at one sign.
Where the sign came from
The radical sign first appeared in print in 1525, in Christoff Rudolff’s algebra book Die Coss — it is a flourished letter r, for the Latin radix, “root”. Rudolff’s √ had no bar; Descartes added the vinculum in 1637, completing the shape copied today.
How to type it
| Platform | Method |
|---|---|
| Windows | Alt + 251 in many apps (legacy code page); Word: 221A then Alt + X always works |
| Mac | Option + V |
| Excel / Sheets | Use the function: =SQRT(16) returns 4; the sign itself pastes as text |
| HTML | √ or √ |
| LaTeX | \sqrt{x} · \sqrt[3]{x} for cube roots |
Explore more
The operator family lives on the math symbols hub; its tolerance partner ± is on the plus minus symbol page, and every sign’s name is listed in the symbol names and meanings guide.
Frequently asked questions
What is √ called?
The radical sign, or the square-root sign. The number under it is the radicand; the whole expression is a radical.
Why does √16 = 4 but √2 never ends?
16 is a perfect square (4 × 4), so its root is whole. √2 ≈ 1.41421356… is irrational — its decimals never terminate or repeat, a fact that famously troubled the Pythagoreans.
How do I write a cube root on a keyboard?
Copy ∛ from this page, or in LaTeX use \sqrt[3]{x}. Most keyboards have no direct cube-root key.
Does the bar over the numbers matter?
Yes — the vinculum groups: √(9 + 16) = √25 = 5, but √9 + 16 = 19. When you type a pasted √ into plain text, brackets do the bar’s job: sqrt(a+b).
What is the root of 0?
0 — 0 × 0 = 0. Negative radicands have no real square root, which is where imaginary numbers (and the letter i) enter.