A while loop can be used to approximate the square root of a value $S$ iteratively.

1. Start with a guess $x$, for example, $x = 0.1 \cdot S$.
2. If $\left|x^2 - a\right| < \epsilon$ for some very small error tolerance $\epsilon$ (epsilon) then $x$ is a good enough solution.
3. Otherwise, a better estimate is $\frac 1 2 \cdot (x + \frac S {x})$.

Repeat steps 2 and 3 until the condition $\left|x^2 - a\right| < \epsilon$ holds.