newton_sqrt.hs

nwSqrt :: Int -> Double
nwSqrt n = let s = sqrts $ fromIntegral n in
  snd $ last $ takeWhile inThreshold $ zip s (tail s)
  where
    sqrts :: Double -> [Double]
    sqrts n = 1.0:[x - (x ^ 2 - n) / (2 * x) | x <- sqrts n]

    inThreshold :: (Double,Double) -> Bool
    inThreshold (a,b) = abs (a - b) > 0.00000001

-- *Main> nwSqrt 2
-- 1.4142135623746899
-- *Main> nwSqrt 3
-- 1.7320508100147276