G'day all.
Quoting Henning Thielemann
http://darcs.haskell.org/htam/src/Numerics/ZeroFinder/Newton.hs
with inverse t (\x->(x^2,2*x)) t
The problem with all such solutions was touched on by Longesh:
20 iterations is a bit arbitrary.
This isn't a one-liner, but there's a straightforward answer to the "arbitrary" number of iterations: Assuming that the task is to compute a square root fast, a better solution is to come up with an initial guess that's good enough such that you only need a fixed number of iterations. This one is as accurate as my CPU's built-in sqrt, and unlike every other solution posted here, it uses no loops: http://www.opensubscriber.com/message/haskell-cafe@haskell.org/5135386.html But, of course, we're now way off-topic from the original question! Cheers, Andrew Bromage