The "divide" and "average" method, and old-time method for approximating the square root of any positive number, can be formulated as
![x=((x+a/x))/(2)](https://img.qammunity.org/2022/formulas/mathematics/college/dnfmja597lj4asuxfgn5z55wz9j197azfd.png)
where
is the number whose square root we need to find.
Estimate the error in approximation as
![\varepsilon =\left | (x_(new)-x_(old))/(x_new) \right |](https://img.qammunity.org/2022/formulas/mathematics/college/1g2zfiokewd4pjfvg01shquh4279i6wsih.png)
Repeat this loop until this
is less than or equal to the specified value.