' version 14-01-2019
' compile with: fbc -s console

Function nth_root(n As Integer, number As Double) As Double

    Dim As Double a1 = number / n, a2 , a3

    Do
        a3 = Abs(a2 - a1)
        a2 = ((n -1) * a1 + number / a1 ^ (n -1)) / n
        Swap a1, a2
    Loop Until Abs(a2 - a1) = a3

    Return a1

End Function

' ------=< MAIN >=------

Dim As UInteger n
Dim As Double tmp

Print
Print "   n    5643 ^ 1 / n     nth_root ^ n"
Print " ------------------------------------"
For n = 3 To 11 Step 2
    tmp = nth_root(n, 5643)
    Print Using " ###    ###.########    ####.########"; n; tmp; tmp ^ n
Next

Print
For n = 25 To 125 Step 25
    tmp = nth_root(n, 5643)
    Print Using " ###    ###.########    ####.########"; n; tmp; tmp ^ n
Next

' empty keyboard buffer
While Inkey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End