The "divide" and "average" method, and old-time method for approximating the square root of any positive number, can be formulated as
[tex]x=\frac{(x+a/x)}{2}[/tex]
where
[tex]a[/tex] is the number whose square root we need to find.
Estimate the error in approximation as
[tex]\varepsilon =\left | \frac{x_{new}-x_{old}}{x_new} \right |[/tex]
Repeat this loop until this [tex]\varepsilon[/tex] is less than or equal to the specified value.
