Answer
$\approx 2.82842$
Work Step by Step
We apply the given recursive formula to find the approximate value for $\sqrt 8$ as follows:
$$\displaystyle a_0=2 \\a_1=\frac{1}{2}(a_0+\frac{8}{a_0})=3\\a_2=\frac{1}{2}(a_1+\frac{8}{a_1})\approx2.8333 \\a_3=\frac{1}{2}(a_2+\frac{8}{a_2})\approx2.82843\\a_4=\frac{1}{2}(a_3+\frac{8}{a_3})\approx2.82842\\a_5=\frac{1}{2}(a_4+\frac{8}{a_4})\approx 2.82842$$
Therefore, we get the approximate value for $\sqrt{8}=2.82842712475 \approx 2.82842$.
