How to Type the Square Root Symbol (√): Windows, Mac, Word, Excel & Mobile Shortcuts

Square Root Symbol Keyboard Shortcut Matrix

Whether you are solving quadratic equations in STEM coursework, drafting engineering design documents, formatting mathematical formulas in Microsoft Word, or coding computational algorithms in Python, JavaScript, or LaTeX, the square root sign (√, also known as the radical symbol) is a fundamental mathematical glyph. Below is your complete platform cheat sheet:

How to Type the Square Root Symbol on Windows (5 Methods)

Windows personal computers offer multiple hardware and software methods to generate the square root symbol (√). Depending on whether your workstation features a full desktop mechanical keyboard with a numeric keypad, a compact ultra-thin laptop, or a touchscreen tablet, choose the most suitable method below:

Method 1: Windows Alt Code (Numeric Keypad — Alt 251)

The standard legacy hardware Alt code for the square root sign is Alt + 251 (based on OEM Code Page 437). In Unicode-aware environments and modern Microsoft Office programs, you can also use Alt + 8730:

Method 2: Windows Emoji & Symbol Panel (Win + .)

For lightweight laptops without a physical numeric keypad (such as Dell XPS, Surface Laptop, HP Envy, Lenovo ThinkPad):

Method 3: Windows Character Map (charmap.exe)

If working offline or inside restricted virtual desktop environments:

• Press Win + R, type charmap, and hit Enter.
• Check the Advanced view box at the bottom.
• In the Search for: box, type square root and click Search.
• Double-click the √ symbol, click Copy, and paste it (Ctrl + V) into your document.

How to Type the Square Root Symbol on Mac (macOS)

Apple macOS provides the simplest and fastest universal keyboard shortcut for the square root symbol across the entire operating system ecosystem:

Simply hold down the Option (⌥) key and press the letter V. The √ symbol will appear immediately. This shortcut functions identically across US, UK, European, Canadian, Australian, and international Mac keyboards in every native application (Pages, Numbers, Keynote, Safari, TextEdit, Mail, and Terminal).

Method 2: macOS Character Viewer (Ctrl + Cmd + Space)

If you prefer a visual palette on Apple macOS:

• Press Ctrl + Cmd + Space to open the Character Viewer.
• Type square root or radical in the search bar.
• Double-click the √ glyph, or choose related mathematical root variants like the cube root (∛) and fourth root (∜).

How to Type Square Root in Microsoft Word, Excel & PowerPoint

Microsoft 365 and Office applications feature rich mathematical equation formatting engines alongside standard text entry shortcuts:

Microsoft Word (3 Methods)

• Unicode Alt+X Hex Code (Fastest in Text): Type 221A (or 221a) directly in your document body and immediately press Alt + X. Word will automatically convert the hexadecimal string into the √ radical symbol.
• Word Equation Editor (Professional Math Typesetting): Press Alt + = to open the Equation Editor container. Type sqrt followed by your radicand in parentheses (e.g. sqrt(x+y)) and press the Spacebar. Word will render a publication-grade radical sign with an extended top vinculum bar: √x+y.
• Ribbon Menu: Navigate to Insert → Symbol → More Symbols. Under the Subset dropdown, select Mathematical Operators, highlight the square root sign (√), and click Insert.

Microsoft Excel (Calculations & Symbol Display)

Depending on whether you want to calculate mathematical square roots or display the graphical symbol in spreadsheet labels:

• Calculate Square Root Value: Use the standard Excel formula =SQRT(number) or =SQRT(A1). For example, =SQRT(144) outputs 12.
• Exponential Calculation Formula: You can also use the power operator: =(A1)^(1/2) or =POWER(A1, 0.5). For cube roots, use =(A1)^(1/3).
• Display the √ Symbol in Formulas: Enter the formula =UNICHAR(8730) to return the visual √ character in a cell. For combined text labels, write =UNICHAR(8730) & "64 = " & SQRT(64), which outputs √64 = 8.

How to Insert Square Root in Google Docs & Google Sheets

Google Docs

• Equation Tool: Click Insert → Equation from the top navigation bar. In the equation toolbar that appears, click the Square Root icon (or type sqrt followed by Enter) to insert an expanding radical sign with a top horizontal bar.
• Special Characters: Click Insert → Special characters. In the search box on the right, type square root, or draw the symbol in the canvas box, then click the √ character.

Google Sheets

• Calculation Formula: Enter =SQRT(cell_reference) (e.g. =SQRT(49) returns 7).
• Symbol Formula: Enter =UNICHAR(8730) to display the raw √ symbol.

How to Type Square Root on iPhone, iPad & Android

iOS (Apple iPhone and iPad)

On standard iOS virtual keyboards, the square root symbol is located within mathematical symbol pages:

• Tap the 123 key in the bottom-left corner.
• Tap the #+= key to navigate to the secondary symbols page.
• Look for the √ symbol or use the 1-click copy box at the top of this guide to copy and paste it into iMessage, WhatsApp, Notes, or Safari.

Android (Google Gboard & Samsung Keyboard)

• Tap the ?123 key to switch to numbers.
• Tap the =< key (or 1/2 on Samsung) to open the extended mathematical symbols palette.
• Tap the dedicated √ key located in the top or middle row.

Developer & Technical Reference (Unicode, HTML, CSS, Python & LaTeX)

For software developers, computer scientists, web designers, and LaTeX authors, below is the comprehensive technical encoding cheat sheet for the square root sign and higher-order radical roots:

Mathematical Notation Rules, Radical Anatomy & Arithmetic Properties

Proper mathematical notation and scientific typesetting require understanding the formal anatomical components of radical expressions and the core algebraic axioms governing roots in algebra, pre-calculus, and physics:

Anatomy of a Radical Expression

In standard mathematical typography, a complete radical expression consists of four distinct anatomical components:

• Radical Symbol (√): The fundamental mathematical operator indicating that an nth root is to be extracted.
• Radicand: The numeric constant, algebraic term, or polynomial expression placed beneath or immediately following the radical symbol (for example, in $\sqrt{x^2 + 1}$, the entire expression $x^2 + 1$ is the radicand).
• Vinculum: The horizontal overline bar extending continuously across the top of the radicand. The vinculum acts as a grouping grouping delimiter (parenthesis). In mathematical formatting without a vinculum, parentheses must always be written to prevent operational ambiguity (e.g., write √(x + y) rather than √x + y, which strictly represents (√x) + y).
• Index (Degree of the Root): The small superscript number resting in the crook of the radical sign indicating which root is being evaluated (e.g., $3$ in $\sqrt[3]{x}$ for the cube root, or $4$ in $\sqrt[4]{x}$ for the fourth root). When no index number is written, the degree is universally understood to be $2$ (the standard square root).

Principal Square Root vs. Plus-or-Minus ($pm$)

By strict international mathematical definition, the radical symbol √ refers exclusively to the principal (non-negative) square root of a real number. Therefore, $\sqrt{25} = 5$ (and never $-5$). When solving quadratic or polynomial equations such as $x^2 = 25$, two independent roots exist, which must be formally denoted using the plus-or-minus operator: $x = \pm\sqrt{25} = \pm 5$.

Fundamental Algebraic Rules of Radicals

When simplifying algebraic expressions, computational algorithms, and calculus derivatives, four foundational transformation rules apply:

Origin & Historical Evolution of the Radical Sign (√)

The modern square root symbol √ has a rich mathematical heritage spanning over five centuries. In medieval Latin mathematical manuscripts, mathematicians wrote the word radix (Latin for "root") or abbreviated it as a capital letter R with a stroke (similar to the medical prescription symbol ℞).

In 1525, German mathematician Christoph Rudolff published the first German-language algebra textbook, Die Coss. To save printing space, Rudolff introduced the stylized lowercase cursive letter r without the top bar to represent square roots (√).

Over a century later, in 1637, French philosopher and mathematician René Descartes introduced the extended horizontal bar (the vinculum) connected to Rudolff's radical sign in his landmark treatise La Géométrie, creating the modern radical symbol (√ x ) universally recognized across all scientific disciplines today.

Frequently Asked Questions About the Square Root Symbol