# Number - Root function

## About

The root function is the inverse operation of the exponentiation.

- With the below exponentiation of the base b to the power of n

<MATH> b^n = a </MATH>

- the base b can be defined back with the root function as:

<MATH> b = \sqrt[n]{a} = a^{\frac{1}{n}} </MATH>

If you need to get the exponent n (power), the operation is not the root function but the logarithm <MATH> n = log_b(a) </MATH>

## Articles Related

## Custom

### Square Root

square root is the inverse of the square operation

- If

<MATH> y^2 = x </MATH>

- then

<MATH> y^{\frac{1}{2}} = \sqrt[2]y = \sqrt{y} = x </MATH>

Every positive number x has two square roots:

- a positive number known as the principal square root and denoted:
- <math>\sqrt {x}</math>
- or <math>x^{\frac{1}{2}}</math> in exponent notation

- a negative number:
- <math>-\sqrt {x}</math>
- or <math>-x^{\frac{1}{2}}</math>

For example: The square roots of 9 are:

- 3 denoted as <math>\sqrt9</math>
- and −3 denoted as <math>-\sqrt9</math>