Remember that the nth root of a number x is x^(1/n).

So all you need is a universal power function:

program root_n;

function raise(man : real; expt : real):real;
begin
  raise:=(exp(expt*ln(man)));
end;

begin
  writeln('The square root of 2 is ',raise(2,1/2));
  writeln('The 10th root of 2344 is ',raise(2344,1/10));
end.

Thanks,
-Larry

???? The Individual Leungl (ucsub.colorado.edu)
?????? wrote on 18 Mar 96
???? about ? Need help finding root ? :

USES Crt;
VAR a, b    :  REAL;
    Result  :  REAL;

FUNCTION Root(e, n : REAL) : REAL;
  BEGIN
    IF (n < 0) AND (e <> 0) AND (e = Int(e)) AND
      (Odd(Trunc(e)) = TRUE)
      THEN Root := -(EXP(LN(ABS(n))/e))
    ELSE IF (n = 0) AND (e <> 0) THEN
      Root := 0
    ELSE IF e = 1 THEN
      Root := e
    ELSE
      Root := EXP(LN(n)/e);
  END;

BEGIN
  ClrScr;
  a := 3;
  b := 125;
  Result := Root (a, b);  { Result=5, because 5^3=125 }
  Write (Result:10:3);
END.

A root of a number! All you need is the generic power function
covered in

 93045 Jan 1 09:31 ftp://garbo.uwasa.fi/pc/link/tsfaqp.zip
 tsfaqp.zip Common Turbo Pascal Questions and Timo's answers

If you need the root of a polynomial, that's much more complicated.
The late TP 4.0 numerical analysis toolbox included a good source.
You might also check (no guarantees)

 303775 May 1 1991 ftp://garbo.uwasa.fi/pc/turbopas/nrpas13.zip
 nrpas13.zip Numerical Recipes Pascal shareware version, 303K!

   All the best, Timo

the n-th root of x you can calculate like this
exp(1/n*ln(x))
because

n  /--
-\/ x  =x^(1/n)=exp(1/n*ln(x))

So, I think this helps you to write your function.