Calculating the square root of x/sandbox

Try your hand on Newton's method

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 clicks of the "save" button:

{{subst:square root|17|3}}

Sandbox

{{subst:square root|100|10}}
10
10
10
10.000000000311
10.000078883626
10.039798887949
10.932861993477
15.351851851852
27
51.22
100
4.1231056256177
4.12310562562
4.12310562562
4.12310562562
4.12310562562
4.12310562562
4.12310562562
4.12310877528
4.1282051282
4.33333333333
3