Radical Symbol (√)
The Universal Square Root Symbol in Mathematics
Click to copy the square root symbol
Essential Root Symbols
About the Square Root Symbol
The radical symbol (√), also known as the square root symbol, is one of the most fundamental mathematical operators. Introduced in 1525 by German mathematician Christoff Rudolff, it has become the universal symbol for representing square roots in mathematics, science, and engineering worldwide.
Symbol Details
U+221A Unicode Character "SQUARE ROOT"
\sqrt LaTeX Command for Square Root Symbol
√ HTML Entity for Square Root
Mathematical Operator Square Root and Radical Symbol Classification
Components of the Square Root Symbol
- Vinculum: The horizontal line above the expression
- Radical Sign: The √ symbol itself
- Index: Optional degree number (2 for square root is implicit)
- Radicand: The expression under the square root symbol
How to Type the Radical Symbol (√)
There are several ways to type the radical symbol (√) depending on your device and operating system. Here are the most common methods for different platforms:
Windows
Alt Code Method
- → Hold Alt key
- → Type 251 on numeric keypad
- → Release Alt key
Character Map
- → Open Character Map (charmap.exe)
- → Find and select √
- → Click Copy
Word/Office
- → Type 221A
- → Press Alt + X
Mac
Keyboard Shortcut
- → Press Option + v
Character Viewer
- → Press Control + Command + Space
- → Search for "square root"
- → Double-click to insert
Text Replacement
- → Go to System Preferences > Keyboard > Text
- → Add "sqrt" as a replacement for √
Mobile Devices
Math Keyboard
- → Switch to math/symbol keyboard
- → Find √ in symbols section
Text Replacement
- → Type "sqrt" or "/sqrt"
- → Select √ from suggestions
Copy & Paste
- → Copy √ from a website or document
- → Paste where needed
Mathematical Examples
Basic Operations
- • √25 = 5
- • ∛27 = 3
- • ∜16 = 2
- • √(n²) = |n|
- • √2 ≈ 1.414
Advanced Applications
- • √(x² + y²)
- • √(-1) = i
- • x = (-b ± √(b² - 4ac)) / 2a
Scientific Applications
Physics
- • V_RMS = √(V_peak/√2)
- • KE = ½mv²
Statistics
- • σ = √(Σ(x - μ)²/N)
Frequently Asked Questions
Q What is the radical symbol called?
The radical symbol (√) is also known as the square root sign, root symbol, or radix. It comes from the Latin word 'radix' meaning 'root'.
Q Why can't I see the radical symbol on my device?
If you see a box or question mark instead of √, your device might not have the proper font support. Try updating your system fonts or switching to a different font that supports mathematical symbols.
Q Can I use the radical symbol in Microsoft Word?
Yes, you can insert the radical symbol in Word through: 1) The equation editor, 2) Alt + 251 on the numeric keypad, or 3) Typing 221A and pressing Alt + X.
Q How do I type the radical symbol on my phone?
You can type the radical symbol on mobile devices by using a mathematical keyboard app, copying and pasting the symbol, or setting up text replacement shortcuts in your keyboard settings.
Q What's the difference between √ and ∛?
√ represents a square root (second root), while ∛ represents a cube root (third root). The square root is used more commonly and doesn't require an index number.
Q Is the radical symbol universal?
Yes, the radical symbol (√) is universally recognized in mathematics across different languages and cultures, making it one of the most standardized mathematical symbols.
Q Can I use the radical symbol in programming?
While you can use √ in comments and strings, most programming languages use functions like Math.sqrt() or math.sqrt() for square root calculations instead of the symbol itself.
Q How do I write other roots like fourth root?
For roots other than square root, you can use the nth root symbol (∛ for cube root, ∜ for fourth root) or add a small number (index) before the radical symbol to indicate the root degree.
Mathematical Symbols Library
| Symbol | Name | Description | Example |
|---|---|---|---|
| = | Equal Sign | Equality | 3 = 1 + 2 |
| ≠ | Not Equal Sign | Inequality | 10 ≠ 6 |
| < | Less Than | Strict Inequality | 7 < 10 |
| > | Greater Than | Strict Inequality | 6 > 2 |
| ≤ | Less Than or Equal | Inequality | x ≤ y |
| ≥ | Greater Than or Equal | Inequality | a ≥ b |
| ≈ | Approximately Equal | Almost Equal To | π ≈ 3.14159 |
| ≡ | Identical To | Identity | (a+b)² ≡ a²+2ab+b² |
| + | Plus Sign | Addition | 4 + 5 = 9 |
| − | Minus Sign | Subtraction | 5 − 2 = 3 |
| × | Times Sign | Multiplication | 4 × 3 = 12 |
| ÷ | Division Sign | Division | 15 ÷ 5 = 3 |
| ± | Plus-Minus | Both Plus and Minus Operations | 5 ± 3 = 8 and 2 |
| ∓ | Minus-Plus | Both Minus and Plus Operations | 1 ∓ 4 = -3 and 5 |
| ∙ | Multiplication Dot | Multiplication | 2 ∙ 3 = 6 |
| * | Asterisk | Multiplication | 2 * 3 = 6 |
| / | Division Slash | Division | 6/2 = 3 |
| % | Modulo | Remainder | 7 % 3 = 1 |
| √ | Square Root | Square Root Operation | √25 = 5 |
| ∛ | Cube Root | Cube Root Operation | ∛27 = 3 |
| ∜ | Fourth Root | Fourth Root Operation | ∜16 = 2 |
| ⁿ√ | nth Root | nth Root Operation | ⁴√16 = 2 |
| [ ] | Brackets | Calculate Expression Inside First | [2×5] + 7 = 17 |
| ( ) | Parentheses | Calculate Expression Inside First | 3 × (3 + 7) = 30 |
| { } | Braces | Set Notation | {x | x > 0} |
| ⟨ ⟩ | Angle Brackets | Vector Notation | ⟨x,y,z⟩ |
| % | Percent | 1% = 1/100 | 10% × 30 = 3 |
| ‰ | Per-mille | 1‰ = 1/1000 | 10‰ × 30 = 0.3 |
| ppm | Per-million | 1 ppm = 1/1000000 | 10ppm × 30 = 0.0003 |
| ppb | Per-billion | 1 ppb = 1/1000000000 | 10 ppb × 30 = 3×10-7 |
| ∧ | And | Logical AND | x ∧ y |
| ∨ | Or | Logical OR | x ∨ y |
| ¬ | Not | Logical Negation | ¬x |
| ⇒ | Implies | Implication | p ⇒ q |
| ⇔ | Equivalent | If and Only If (IFF) | p ⇔ q |
| ∀ | For All | Universal Quantifier | ∀x P(x) |
| ∃ | There Exists | Existential Quantifier | ∃x P(x) |
| ⊕ | XOR | Exclusive OR | p ⊕ q |
| ∈ | Element Of | Set Membership | 2 ∈ {1,2,3} |
| ∉ | Not Element Of | Negation of Set Membership | 0 ∉ {1,2,3} |
| ⊂ | Subset | Proper Subset | {1,2} ⊂ {1,2,3} |
| ⊆ | Subset or Equal | Subset or Equal To | {1,2} ⊆ {1,2} |
| ∪ | Union | Set Union | A ∪ B |
| ∩ | Intersection | Set Intersection | A ∩ B |
| ∅ | Empty Set | Null Set | ∅ = {} |
| ∖ | Set Difference | Relative Complement | A ∖ B |
| ∫ | Integral | Integration | ∫x dx = x²/2 + C |
| ∂ | Partial Derivative | Partial Differentiation | ∂z/∂x |
| ∑ | Summation | Sum of Series | ∑(1/n²) |
| ∏ | Product | Product of Series | ∏(1/n) |
| ∞ | Infinity | Infinity Symbol | lim(x→∞) |
| ∇ | Nabla | Gradient/Divergence | ∇f |
| δ | Delta | Small Change | δx |
| Δ | Delta | Finite Change | Δx |
| α | Alpha | Greek Letter Alpha | α + β = γ |
| β | Beta | Greek Letter Beta | β = 2α |
| γ | Gamma | Greek Letter Gamma | γ = 3 |
| π | Pi | Pi Constant | π ≈ 3.14159 |
| θ | Theta | Greek Letter Theta | sin(θ) |
| λ | Lambda | Greek Letter Lambda | λx.x+1 |
| μ | Mu | Greek Letter Mu | μ = 2.5 |
| σ | Sigma | Greek Letter Sigma | σ² |
| ∠ | Angle | Angle Symbol | ∠ABC = 90° |
| ⊥ | Perpendicular | Perpendicular Lines | l ⊥ m |
| ∥ | Parallel | Parallel Lines | l ∥ m |
| △ | Triangle | Triangle Symbol | △ABC |
| □ | Square | Square Symbol | □ABCD |
| ∘ | Composition | Function Composition | f ∘ g |
| ° | Degree | Degree Symbol | 90° |
| ≅ | Congruent | Congruence | △ABC ≅ △DEF |