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Re:Being recruited in the USA by pjscott on Wednesday January 04, 2012 @06:34PM (#3426512)
Easier to remember is the bisection method: essentially, a binary search for where the graph crosses the x-axis. It's what I would have pulled out if I got asked the square root problem in an interview:

http://en.wikipedia.org/wiki/Bisection_method

Re:Being recruited in the USA by sgk284 on Thursday January 05, 2012 @02:42AM (#3427862)
Interestingly enough, I recently wrote a post explaining how to take a binary search and derive Newton's method from it: http://stevekrenzel.com/articles/newtons-law

It's a fairly straight-forward transformation.