# 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

[edit | edit source]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

[edit | edit source]### Step-by-step

[edit | edit source]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

[edit | edit source]{{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

[edit | edit source]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.