this is a method that can be used to approximate an irrational number of the form a + sqrt(b) pretty quickly. It can be modified to let it calculate pure square roots in an interesting way: if you put in 0 for a and n for b, hoping to get 0 + sqrt(n), it will unfortunately not converge, but instead cycle between two or three values. However, if you put in 1 for a and n for b, it will converge to 1 + sqrt(n), and all you have to do is subtract 1 from the result it converges to. enjoy! this doesn't use much math besides algebra.
