def sqrt n
  g, avg = 1
  loop {
    q = n / g
    avg = (q + g) / 2.0
    (avg-g).abs <= 0.000001 ? break : g = avg
  }
  avg
end

sqrt 9999*9999
sqrt 0.00000000000000000000000001
puts sqrt(1.0e+24) == 1000000000000.0