Square Root Symbol (√): What It Means, Its Name, and How to Type It
The √ symbol is the radical sign, and it asks one question: what number times itself gives the value sitting under it? So √9 = 3, because 3 × 3 = 9. This guide names every part of the symbol, lists the perfect squares, and shows how to type √ on Windows, Mac, in HTML, and in LaTeX.
The √ symbol is the radical sign. It asks one question: what non-negative number, multiplied by itself, gives the value sitting underneath it? That value is the radicand, the answer is the square root, and a bare √ always means the principal, non-negative root.
Try it on any number with our square root calculator.
What the parts of the symbol are called
The full expression has three named pieces. The √ itself is the radical sign, sometimes called the radical symbol or the surd. The number tucked under the sign is the radicand. A small number in the notch in front of the sign is the index, and for a square root that index is left unwritten by convention.
What a square root actually is
A square root is the inverse of squaring. Squaring multiplies a number by itself, and taking the square root undoes that. Formally, √a is the non-negative number whose square is a.
When the radicand is a perfect square, the answer is a clean whole number. Each row below pairs the expression with the multiplication that proves it.
Most radicands are not perfect squares, so their roots run on forever. When that happens, the value is irrational and you can only approximate it.
√2 ≈ 1.41421 √10 ≈ 3.16228
To get a value like that without a calculator, you can find a square root by hand.
How to type the square root symbol
Every method produces the same glyph. The √ character lives at one Unicode code point, so pick whichever route matches the tool you are in.
Menu routes work everywhere, including laptops without a numeric keypad. In Google Docs use Insert then Special characters and search "square root," or Insert then Equation and type the LaTeX command. In Microsoft Word use Insert then Symbol then More Symbols under the Mathematical Operators subset, or Insert then Equation.
The numpad shortcut needs real hardware. Alt and the keypad digits only work with a physical numeric keypad and Num Lock on, which is why laptop users often fall back to the Insert Symbol menu or copy the character directly. In LaTeX the command stretches the radical sign and bar over whatever sits inside the braces, so it covers a whole expression rather than just the first term.
√ vs ∛ vs the general radical
The radical sign changes meaning with the index in its notch. A square root, a cube root, and the general nth root all use the same sign with a different index.
Square roots are just the most common case. The nth root of a is the number that, raised to the power n, gives a. A square root is that rule with the index equal to two, common enough that the index is dropped. So a bare √ with no small number in front always reads as a square root.
The short version
A bare √ means the square root, the value under it is the radicand, and the small number in front is the index. The sign returns the principal, non-negative root, and the same glyph types from Alt, Option, an HTML entity, or a LaTeX command depending on where you are working. Square roots show up constantly in geometry, so the distance between two points and the length of a right triangle's hypotenuse both come straight out of a radical sign, which is exactly what our Pythagorean theorem calculator returns.
Common questions
The horizontal bar stretching across the top of the radicand is the vinculum. It works like grouping brackets: everything beneath it belongs to the radicand. The vinculum is what shows where the root stops, so it tells √(a + b) apart from √a + b.
No. The radical sign returns the principal root, which is the non-negative one. The plus-or-minus only appears when you solve a quadratic equation yourself, where both the positive and negative value square back to the radicand. The symbol √ on its own always means the positive root.
There is no real number whose square is negative, since any real number squared is zero or positive. So the square root of a negative has no real value and is defined using the imaginary unit i. These results belong to the complex numbers rather than the real number line.
