The approximate value of $\frac{1}{3\sqrt{8.08}}$ is

$$\begin{gathered} \mathrm{x}=8 \mathrm{\delta x}=0.08 \\ \mathrm{f}\left(\mathrm{x}\right)=\frac{1}{3\sqrt{\mathrm{x}}} \\ \mathrm{f}(\mathrm{x}+\mathrm{\delta x})={\mathrm{f}}^1\left(\mathrm{x}\right).\mathrm{\delta x}+\mathrm{f}\left(\mathrm{x}\right) \\ =\frac{-1}{3} {\mathrm{x}}^{-4/3}.(0.08)+\frac{1}{2} \\ =\frac{-1}{48}\times 0.08+\frac{1}{2} \\ =\frac{1}{2}-\frac{0.01}{6} \\ =0.5-0.00167 \\ =0.4984 \end{gathered}$$