unfinished on converting between Doubles, http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Decimal_.28base_10.29

sqrt.hs

module Sqrt () where

import Data.List

data MyDouble = MD Integer [Integer]
data MyDouble1 = MD1 Integer [Integer]

-- TO DO
toMyDouble :: Double -> MyDouble
toMyDouble = undefined

-- TO DO
fromMyDouble1 :: MyDouble1 -> String
fromMyDouble1 (MD1 n d) = take 100 $ concatMap show d

getFirst :: MyDouble -> Integer
getFirst (MD _ d) = head [x | x <- [9,8..0], x * x <= head d]

getNext :: Integer -> Integer -> Integer -> Integer
getNext remainder upward result = head [x | x <- [9,8..0], x * (result * 20 + x) <= remainder * 100 + upward]

getNexts :: Integer -> [Integer] -> Integer -> [Integer]
getNexts remainder upwards result = a : getNexts r1 (tail upwards) re1
  where a = getNext remainder (head upwards) result
        r1 = remainder * 100 + head upwards - (result * 20 + a) * a
        re1 = result * 10 + a

mySqrt1 :: MyDouble -> MyDouble1
mySqrt1 md@(MD a b) = MD1 c d
  where  c = a
         d = e : getNexts (head b - e * e) (tail b) e
         e = getFirst md

getDigits :: MyDouble1 -> [Integer]
getDigits (MD1 _ a) = a

mySqrt :: Double -> String
mySqrt = fromMyDouble1 . mySqrt1 . toMyDouble

http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Decimal_.28base_10.29

2 in MyDouble looks like MD 1 (2:[00,00..]), which has a two digits' Integer list.
MyDouble1 has a single digit Integer list.