The approximate value of \(\sqrt[3]{0 \cdot 026}\) is

Let \(\mathrm{f}(x)=\sqrt[3]{x}=x^{\frac{1}{3}}\)
\(\therefore \quad \mathrm{f}^{\prime}(x)=\frac{1}{3} x^{-\frac{2}{3}}=\frac{1}{3 x^{\frac{2}{3}}}\)
Here, \(\mathrm{a}=0.027\) and \(\mathrm{h}=-0.001\)
\(\begin{aligned}
& \therefore \quad f(a)=f(0.027)=(0.027)^{\frac{1}{3}}=0.3 \text { and } \\
& \mathrm{f}^{\prime}(\mathrm{a})=\mathrm{f}^{\prime}(0.027) \\
& =\frac{1}{3(0.027)^{\frac{2}{3}}} \\
& =\frac{1}{3(0.09)}=\frac{1}{0.27} \\
& \therefore \quad \mathrm{f}(\mathrm{a}+\mathrm{h}) \approx \mathrm{f}(\mathrm{a})+\mathrm{hf}^{\prime}(\mathrm{a}) \\
& \approx 0.3-\frac{0.001}{0.27} \\
& \approx 0.3-0.0037 \\
& \approx 0.2963
\end{aligned}\)