' Nth root
DECLARE FUNCTION NthRoot (N%, X#, Precision#) AS DOUBLE
X# = 144
PRINT "Finding the nth root of ";X#;" to 6 decimal places"
PRINT "  x      n        root    x ^ (1 / n)"
PRINT "--------------------------------------"
FOR I% = 1 TO 8
  PRINT FORMAT$("%3d   ", X#);
  PRINT FORMAT$("%4d    ", I%);
  PRINT FORMAT$("%10.6f", NthRoot(I%, X#, .0000001));
  PRINT FORMAT$("    %10.6f", X# ^ (1 / I%))
NEXT I%
input X#
END

FUNCTION NthRoot (N%, X#, Precision#) AS DOUBLE
  ' Returns the Nth root of value X to stated Precision
  X0# = X#
  X1# = X# / N% ' initial guess
  WHILE ABS(X1# - X0#) > Precision#
    X0# = X1#
    X1# = ((N% - 1) * X1# + X# / X1# ^ (N% - 1)) / N%
  WEND
  NthRoot = X1#
END FUNCTION