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Square Root

Tool to compute and simplify a square root. The square root for a number N, is the number noted sqrt(N) that, multiplied by itself, equals N.

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Square Root -

Tag(s) : Symbolic Computation, Functions

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Square Root

Square Root Calculator





See also: Cube RootCalculator

Expression with Square Root Simplification


Batch Square Root Computation


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See also: Cube RootCalculator

Answers to Questions (FAQ)

How to calculate a square root?

The dCode square root calculator allows both positive or negative numbers (thus having complex roots) and returns answers with an exact value or an approximate value (the precision can be adjusted by defining a minimum number of significant digits)

Example: $ \sqrt{4} = 2 $ and $ \sqrt{-1} = i $

How to simplify a square root?

Root calculations have properties similar to exponentiation:

$$ \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \\ \sqrt{ \frac{a}{b} } = \frac{\sqrt{a}}{\sqrt{b}} $$

For any positive real number $ a \in \mathbb{R}_+^* $

$$ \sqrt{a^2} = a \\ \left( \sqrt{a} \right)^2 = a $$

Therefore

$$ \sqrt{a^2 \times b} = a \sqrt{b} $$

How to simplify a fraction with square root?

If the denominator is a radical, then multiply the numerator and the denominator by it to make it disappear.

$$\frac{a}{\sqrt{b}} = \frac{a\sqrt{b}}{\sqrt{b}^2} = \frac{a\sqrt{b}}{b} $$

If the denominator is an addition or subtraction of roots, then apply the remarkable identity: $ (a+b)(a-b) = a^2-b^2 $

$$ \frac{a}{\sqrt{b}+\sqrt{c}} = \frac{a(\sqrt{b}-\sqrt{c})}{(\sqrt{b}+\sqrt{c})(\sqrt{b}-\sqrt{c})} = \frac{a\sqrt{b}-a\sqrt{c}}{b-c} $$

$$ \frac{a}{\sqrt{b}-\sqrt{c}} = \frac{a(\sqrt{b}+\sqrt{c})}{(\sqrt{b}-\sqrt{c})(\sqrt{b}+\sqrt{c})} = \frac{a\sqrt{b}+a\sqrt{c}}{b-c} $$

How to write a square root?

In Unicode format there is the character (U+221A).

In computer formulas, sqrt() function is most often used.

Terms root, radix ou radicand sont équivalents.

What doest sqrt means?

The word sqrt is generally used in the formula to indicate a square root, the word comes from the contraction of square root.

Example: sqrt(2) = $ \sqrt{2} $

What is a square number?

A square number is the square of an integer.

Example: $ 3 $ is an integer, $ 3^2 = 3 \times 3 = 9 $ then $ 9 $ is a square number.

If the square root of a number $ x $ is an integer, then $ x $ is a square number.

Source code

dCode retains ownership of the online 'Square Root' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any 'Square Root' algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any 'Square Root' function (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and no data download, script, copy-paste, or API access for 'Square Root' will be for free, same for offline use on PC, tablet, iPhone or Android ! dCode is free and online.

Need Help ?

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Questions / Comments

Thanks to your feedback and relevant comments, dCode has developed the best 'Square Root' tool, so feel free to write! Thank you!


Source : https://www.dcode.fr/square-root
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