Question

Evaluate $\sqrt[3]{27}+\sqrt[3]{0.008}+\sqrt[3]{0.064}$

Answer 1

Given $\sqrt[3]{27}+\sqrt[3]{0.008}+\sqrt[3]{0.064}$

Where $\sqrt[3]{27}=3$

Consider

$$\begin{gathered} 0.008=\frac{8}{1000} \\ 0.064=\frac{64}{1000} \end{gathered}$$

Hence, $\sqrt[3]{0.008}=\sqrt[3]{\frac{8}{1000}}=\frac{2}{10}$

ans $\sqrt[3]{0.064}=\sqrt[3]{\frac{64}{1000}}=\frac{4}{10}$

Now, consider $\sqrt[3]{27}+\sqrt[3]{0.008}+\sqrt[3]{0.064}$

$$\begin{gathered} 3+\frac{2}{10}+\frac{4}{10} \\ \frac{3\times 10+2+4}{10} \\ \frac{30+2+4}{10} \\ \frac{36}{10} \\ 3.6 \end{gathered}$$

Hence, $\sqrt[3]{27}+\sqrt[3]{0.008}+\sqrt[3]{0.064}$ is $3.6$