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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

## Batch Square Root Computation

### 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.

### 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" source code. Except explicit open source licence (indicated CC / Creative Commons / free), the "Square Root" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "Square Root" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, copy-paste, or API access for "Square Root" are not public, same for offline use on PC, tablet, iPhone or Android ! Remainder : dCode is free to use.

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