Sometime ago I wrote a program that used Newtons Method and derivatives to approximate unknown square roots (say $\sqrt 5$) from known square roots like $\sqrt 4$.I have since lost the calculator and the book I got the equation from. 

Edit Researched a bit let me see if I have this right.

First I start with my known $$\sqrt 4=2$$ then I subtract. Thus. $2-\frac {4-5}{(2(\sqrt (4)}$

Then I take that answer call it $r\_{t1}$ and plug it back in so that I have $r\_{t1} -\frac {{r\_{t1}}^2-5}{2(r\_{t1})}$ Rinse lather repeat..

Right?