Successive approximation was the only method I ever used but I like the direct method from your link. Of course, today the problem with successive approximation is that memorizing multiplication tables are considered “drill and kill” by the Common Core Cultists.
The direct method is also a form of successive approximation, one decimal place at a time. Newton Raphson approximately doubles the number of significant places per iteration. Of course, you never get more figures than the significance of your representation, i.e., about 52 for double and 24 for single, using a computer.