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.



print "Root 125th Root of 5643 Precision .001   ";using( "#.###############",  NthRoot( 125, 5642, 0.001  ))
print "125th Root of 5643 Precision .001   ";using( "#.###############",  NthRoot( 125, 5642, 0.001  ))
print "125th Root of 5643 Precision .00001 ";using( "#.###############",  NthRoot( 125, 5642, 0.00001))
print "  3rd Root of   27 Precision .00001 ";using( "#.###############",  NthRoot(   3,   27, 0.00001))
print "  2nd Root of    2 Precision .00001 ";using( "#.###############",  NthRoot(   2,    2, 0.00001))
print " 10th Root of 1024 Precision .00001 ";using( "#.###############",  NthRoot(  10, 1024, 0.00001))
 
wait
 
function NthRoot( root, A, precision)
  x0 = A
  x1 = A /root
  while abs( x1 -x0) >precision
    x0 = x1
    x1 = x1 / 1.0                                ' force float
    x1 = (( root -1.0) *x1 +A /x1^( root -1.0)) /root
  wend
  NthRoot =x1
end function
 
end