An iterative method of approximating the square root of a number. If $\sqrt{k}$ is required, and x₀ is an initial approximation, then $x_{n+1}=\frac{\left(x_n+\frac{k}{x_n}\right)}{2},$ n = 0,1,2,… will converge to the square root of k. For example, to calculate the square root of 5, using a first approximation of 2, will give $x_1=\frac{\left(2+2.5\right)}{2}=2.25$, x₂=2.23611111…, x₃=2.236067978…, x₄=2.236067978…and $\sqrt{5}=2.236067978\dots$. So this method has found the square root to 8 dp after only three iterations.