Square Root Symbol

Your complete guide to the √ symbol - copy, paste, and learn

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What is the Square Root Symbol?

The square root symbol √ (also known as the radical sign or root symbol) is a mathematical symbol used to indicate the square root operation. When placed before a number, it represents a value that, when multiplied by itself, gives the original number. For example, √9 = 3 because 3 × 3 = 9.

Alternative Names and Descriptions

  • • Radical Sign
  • • Radix
  • • Square Root Sign
  • • Root Symbol
  • • sqrt symbol
  • • Radical Symbol
  • • Check Mark Root
  • • √ Symbol

LaTeX Square Root Symbol

In LaTeX, the square root symbol is one of the most commonly used mathematical symbols. Perfect for academic papers, scientific documents, and mathematical typesetting.

Empty square root symbol:

\sqrt{}

Result:

Basic square root:

\sqrt{x}

Result:

Nth root:

\sqrt[n]{x}

Result:

Example with numbers:

\sqrt{25} = 5

Result:

Complex expression:

\sqrt{a^2 + b^2}

Result:

Tip: Click the copy icon next to each code to instantly copy the LaTeX command to your clipboard.

Symbol Codes

Unicode Information:

  • Unicode: U+221A
  • HTML Entity: √ or √
  • HTML Hex: √
  • CSS Code: \221A

Character Details:

  • Unicode Block: Mathematical Operators
  • UTF-8 Encoding: E2 88 9A
  • UTF-16 Encoding: 221A
  • UTF-32 Encoding: 0000221A

Common Uses of the Square Root Symbol

The square root symbol is fundamental in mathematics and appears in numerous applications across various fields. Here are the most common uses in mathematical contexts:

1. Basic Square Root Operations

Finding the square root of perfect squares and non-perfect squares:

\sqrt{16} = 4
\sqrt{25} = 5
\sqrt{2} \approx 1.414
\sqrt{100} = 10

2. Pythagorean Theorem

Calculating the length of sides in right triangles:

c = \sqrt{a^2 + b^2}

where c is the hypotenuse and a, b are the other sides

3. Quadratic Formula

Solving quadratic equations ax² + bx + c = 0:

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

4. Distance Formula

Calculating the distance between two points (x₁, y₁) and (x₂, y₂):

d = \sqrt{ (x_2 - x_1)^2 + (y_2 - y_1)^2 }

5. Standard Deviation

Measuring spread in statistics:

\sigma = \sqrt{\frac{\sum(x - \mu)^2}{ N}}

where σ is standard deviation, μ is mean, N is sample size

6. Simplifying Radicals

Breaking down square roots into simpler forms:

\sqrt{72} = \sqrt{36 \times 2} = 6\sqrt{2}
\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}

7. Physics Applications

Used in velocity, energy, and wave calculations:

Velocity:

v = \sqrt{2gh}

RMS Voltage:

V_{\text{rms}} = \frac{V_{\text{peak}}}{\ sqrt{2}}

8. Complex Numbers

Finding the magnitude of complex numbers:

|z| = \sqrt{a^2 + b^2}

where z = a + bi

9. Nth Root General Form

The radical symbol represents the nth root when a number n is placed above it:

\sqrt[n]{x}

This means "take the nth root of the number x"

Examples:

\sqrt[3]{8} = 2
\sqrt[4]{16} = 2
\sqrt[5]{32} = 2

10. Geometric Mean

Calculating the geometric mean of two numbers:

\text{GM} = \sqrt{ab}

For n numbers:

11. Root Mean Square (RMS)

Finding the quadratic mean or RMS value:

x_{\text{rms}} = \sqrt{\frac{x_1^2 + x_2^2 + \cdots + x_n^2}{ n}}

Commonly used in signal processing and electrical engineering

12. Circle Radius from Area

Finding the radius when given the area of a circle:

r = \sqrt{\frac{A}{\pi}}

where A is the area and r is the radius

13. Solving Simple Equations

Taking square root of both sides to solve for a variable:

If , then:

x = \pm\sqrt{16} = \pm 4

Frequently Asked Questions

What does the square root symbol mean?
The square root symbol (√) represents a mathematical operation that finds a number which, when multiplied by itself, equals the original number. For example, √16 = 4 because 4 × 4 = 16. It's also called the radical sign or radix.
How do I type the square root symbol on my keyboard?

The easiest method is to copy and paste the symbol directly from this page. For other methods:

  • Mac: Press Option + V
  • Linux: Press Ctrl + Shift + U, then type 221A and press Enter
  • Microsoft Word: Type 221A then press Alt + X
What is the Unicode code for the square root symbol?
The Unicode code for the square root symbol is U+221A. In HTML, you can use √ or √. The UTF-8 encoding is E2 88 9A.
How do I write square root in LaTeX?
In LaTeX, use \sqrt{x} for a square root. For nth roots, use \sqrt[n]{x}. For example, \sqrt{25} produces √25.
Can I use the square root symbol in Excel or Google Sheets?
Yes! You can copy and paste the √ symbol directly into Excel or Google Sheets. For calculations, use the SQRT function: =SQRT(number). For example, =SQRT(16) returns 4.
What's the difference between √ and ∛?
√ is the square root symbol (second root), while ∛ is the cube root symbol (third root). √16 = 4 means 4² = 16, whereas ∛27 = 3 means 3³ = 27. The square root is more commonly used in mathematics.
Is the square root symbol supported on all devices?
Yes, the square root symbol (√) is part of the Unicode standard and is supported on virtually all modern devices, browsers, and operating systems including Windows, Mac, Linux, iOS, and Android. It displays consistently across platforms.
Why is it called a radical sign?
The term "radical" comes from the Latin word "radix," meaning "root." The symbol √ was introduced by mathematician Christoph Rudolff in 1525. The horizontal line extending from the symbol is called the vinculum, which groups the numbers under the radical.
Can square roots be negative?
In real numbers, the principal square root is always non-negative. However, every positive number has two square roots: one positive and one negative. For example, both 5 and -5 are square roots of 25, but √25 specifically refers to the positive root (5). The symbol ±√ is used when both roots are needed.
Where is the square root symbol commonly used?
The square root symbol is used extensively in algebra, geometry (Pythagorean theorem), trigonometry, calculus, statistics (standard deviation), physics (velocity and energy equations), engineering, and computer science. It's one of the most fundamental mathematical operators.