Answer
$\approx 2.236$
Work Step by Step
We apply the given recursive formula to find the approximate value for $\sqrt 5$ as follows:
$$\displaystyle a_0=2 \\ a_1=\frac{1}{2}(a_0+\frac{5}{a_0})\approx2.25 \\a_2=\frac{1}{2}(a_1+\frac{5}{a_1})\approx2.23611 \\ a_3=\frac{1}{2}(a_2+\frac{5}{a_2})\approx2.23606 \\a_4=\frac{1}{2}(a_3+\frac{5}{a_3})\approx2.2423 \\ a_5=\frac{1}{2}(a_4+\frac{5}{a_4})\approx2.236$$
Therefore, we get the approximate value for $\sqrt{5}=2.2360679775 \approx 2.236$.
