Task

Implement the algorithm to compute the principal   nth   root   





A

n





{\displaystyle {\sqrt[{n}]{A}}}

   of a positive real number   A,   as explained at the   Wikipedia page.



      *FLOAT 64
      @% = &D0D
      PRINT "Cube root of 5 is "; FNroot(3, 5, 0)
      PRINT "125th root of 5643 is "; FNroot(125, 5643, 0)
      END
 
      DEF FNroot(n%, a, d)
      LOCAL x0, x1 : x0 = a / n% : REM Initial guess
      REPEAT
        x1 = ((n% - 1)*x0 + a/x0^(n%-1)) / n%
        SWAP x0, x1
      UNTIL ABS (x0 - x1) <= d
      = x0