fitfun[fun_, tofit_, params_, x_, range_] := 
 Module[{steps = 11}, 
  xvals = Range[range[[1]], 
    range[[2]], (range[[2]] - range[[1]])/steps];
  yvals = fun[#] & /@ xvals;
  sol = FindFit[Thread[{xvals, yvals}], tofit, params, x];
  tofit /. sol]
fitfun[x, a Sqrt[x], {a}, x, {0, 1}]