Answer
See below
Work Step by Step
$\sqrt 2\approx1.414213562$
From part a, we have:
$f(x)=\frac{x+\frac{n}{x}}{2}$
$f(1)=\frac{1+\frac{2}{1}}{2}=\frac{3}{2}$
$f(\frac{3}{2})=\frac{\frac{3}{2}+\frac{3}{\frac{3}{2}}}{2}\approx1.4167$
$f(1.4167)=\frac{1.467+\frac{2}{1.467}}{2}\approx1.415$
$f(1.415)=\frac{1.415+\frac{2}{1.415}}{2}\approx1.414$
We can see that the sixth decimal becomes constant starting with the fourth step.
