---
url: >-
  /statelake/scripting-reference/functions-and-procedures/numeric-functions/nthroot.md
---

# NthRoot

The function **NthRoot** returns the result of **aValue** inversely raised to the power of **aN**.

In mathematical terms, **aN** is the exponent value known as the index shown as **a** below, and **aValue** is the radicand shown as **b**.

Using 100 as the sample radicand value, if the exponent value is 2 (10 x 10) -

If the exponent value is 3 ((10 x 10) x 10) -

If the exponent is 4 (((10 x 10) x 10) x 10) -

Using the **NthRoot** function, these all result in 10, and would be written as -

* NthRoot(2, 100)
* NthRoot(3,1000)
* NthRoot(4, 10000)

If the result is a nonsense or imaginary number, the result will be the value **NAN** which is an acronym for Not A Number.

Please also refer to the function [Power](/statelake/scripting-reference/functions-and-procedures/numeric-functions/power) which has similar functionality.

**Declaration**: Function NthRoot(const aN : Integer; const aValue : Extended) : Extended;

Examples follow.

```pascal
procedure ScriptEvent (var Value : variant);
var
  NewInt : integer;
  NewExt, NextExt : extended;
begin
  NewInt := 3;                                     //Looking for the cube root
  NewExt := 1000;
  NextExt := NthRoot(NewInt, NewExt);
  LogInfo('Result =  '+FloatToStr(NextExt));       //Displays 'Result =  10'
  LogInfo('');

  NewInt := 2;
  NewExt := -1;                                    //Returns i (an imaginary number)
  NextExt := NthRoot(NewInt, NewExt);
  LogInfo('Result =  '+FloatToStr(NextExt));       //Displays 'Result =  NAN'
  LogInfo('');

end;
```