Number - Root function

About

The root function is the inverse operation of the exponentiation.

<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>

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:
  • 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>

Documentation / Reference


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