Calculating the square root of a

In this learning project, we learn how to approximate the square root of a number numerically.

Newton's method

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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

Try your hand on Newton's method

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Step-by-step

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Cut and paste the following wikitext into the sandbox, and enter your favourite number and a first (non-zero!) approximation of its square root. See what happen after multiple edit-and-saves:

{{subst:square root|number|first approximation}}

Sandbox

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{{subst:square root|17|4.1231056256177}}
4.1231056256177
4.1231056256177
4.1231056256177
4.1231056256177
4.1231056256177
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


What is going on

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Our calculator-template {{square root}} implements the formula  , which is an instant of the general formula for Newton's method   in the case when the function f(x) is given by  . It solves the equation   numerically, by successive approximations.