Square Root

The Mathematical Symbol "Square Root (√)"

The "Square Root" (√)

The √ symbol, universally recognized as the "Square Root", is one of the fundamental symbols in mathematics, representing the operation to find a number that, when multiplied by itself, yields the given number.

Basics of √

The square root of a number \(x\) is written as √x. For instance, the square root of 9 is 3 because \(3 \times 3 = 9\). It's crucial to note that negative numbers do not have real square roots because a square is always non-negative.

Properties

• The square root of a product is the product of the square roots: √(ab) = √a \times √b
• The square root of a quotient is the quotient of the square roots: √(a/b) = √a / √b
• For positive real numbers, the square root is always positive.

Applications

The square root function is ubiquitous in mathematics, physics, engineering, and many other disciplines. Some applications include:

• Geometry: The Pythagorean theorem, which calculates the length of the hypotenuse in a right triangle.
• Quadratic Equations: Solutions can be represented using the square root function.
• Physics: In calculating distances or speeds using certain equations.

Typing √

In HTML and web-based content, using the √ entity will display the square root symbol. In many word processors and other software, the symbol is readily available in the mathematical or symbols section.

Higher Roots

Beyond the square root, there are also cube roots, fourth roots, and so on. These are represented similarly, but with a small numeral above the radical symbol indicating the degree of the root. For instance, the cube root of 8 is written as \( \sqrt[3]{8} \) and equals 2, as \(2 \times 2 \times 2 = 8\).

Conclusion

The √ symbol signifies a foundational mathematical operation with wide-ranging applications in various scientific and engineering domains. Understanding the concept

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Codes for the √ Symbol

The Symbol	√	copy
Alt Code	Alt 8730	copy
HTML Code	√	copy
HTML Entity	√	copy
CSS Code	\221A	copy
Hex Code	√	copy
Unicode	U+221A	copy

How To Insert the √ Symbol

(Method 1) Copy and paste the symbol.

The easiest way to get the √ symbol is to copy and paste it into your document.

Bear in mind that this is a UTF-8 encoded character. It must be encoded as UTF-8 at all stages (copying, replacing, editing, pasting), otherwise it will render as random characters or the dreaded �.

(Method 2) Use the "Alt Code."

If you have a keyboard with a numeric pad, you can use this method. Simply hold down the Alt key and type 8730. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)

(Method 3) Use the HTML Decimal Code (for webpages).

HTML Text	Output
<b>My symbol: &#8730;</b>	My symbol: √

(Method 4) Use the HTML Entity Code (for webpages).

HTML Text	Output
<b>My symbol: &radic;</b>	My symbol: √

(Method 5) Use the CSS Code (for webpages).

CSS and HTML Text	Output
<style> span:after { content: "\221A";} </style> <span>My symbol:</span>	My symbol: √

(Method 6) Use the HTML Hex Code (for webpages and HTML canvas).

HTML Text	Output
<b>My symbol: &#x221A;</b>	My symbol: √

On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x221A to place the √ symbol on your canvas. For example:

JavaScript Text
const x = "0x"+"E9" ctx.fillText(String.fromCodePoint(x), 5, 5);
Output
√

(Method 7) Use the Unicode (for various, e.g. Microsoft Office, JavaScript, Perl).

The Unicode for √ is U+221A. The important part is the hexadecimal number after the U+, which is used in various formats. For example, in Microsoft Office applications (e.g. Word, PowerPoint), do the following:

Type	Output
221A [Hold down Alt] [Press x]	√ (The 221A turns into √. Note that you can omit any leading zeros.)

In JavaScript, the syntax is \uXXXX. So, our example would be \u221A. (Note that the format is 4 hexadecimal characters.)

JavaScript Text	Output
let str = "\u221A" document.write("My symbol: " + str)	My symbol: √