Calculating the square root of a
From Wikiversity
In this learning project, we learn how to approximate the square root of a number numerically.
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[edit] Newton's method
Newton's method is a basic method in numerical approximations. The idea of Newton's method is to "follow the tangent line" to try to get a better approximation. For more details, see w:Newton's method
[edit] Try your hand on Newton's method
[edit] Step-by-step
Cut and paste the following wikitext into the sandbox, and enter your favourite number and a first (non-zero!) approximation. See what happen after multiple edit-and-saves:
{{subst:square root|number|first approximation}}
[edit] Sandbox
{{subst:square root|17|4.1231056256177}}
4.12310562562
4.12310562562
4.12310562562
4.12310562562
4.12310562562
4.12310562562
4.12310562562
4.12310562562
4.12310562562
4.12310562562
4.12310562562
4.12310562562
4.12310562562
4.12310562562
4.12310562562
4.12310562562
4.12310562562
4.12310562562
4.12310877528
4.1282051282
4.33333333333
3
[edit] What is going on
Our calculator-template {{square root}} implements the formula xn + 1 = (xn + a / xn) / 2, which is an instant of the general formula for Newton's method 
in the case when the function f(x) is given by f(x) = x2 − a. It solves the equation x2 − a = 0 numerically, by successive approximations.
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