Evaluate 3√(13,78)^2+(0.968)^3

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$$\begin{gathered} \mathrm{Given} \\ \sqrt[3]{{\left(13.78\right)}^2+{\left(0.968\right)}^3} \\ \mathrm{let} , {\left(13.78\right)}^2=\mathrm{x} \\ \mathrm{taking} \log \mathrm{both} \mathrm{sides}, \\ 2\log \left(13.78\right)=\mathrm{logx} \\ \mathrm{from} \log \mathrm{table}, \log \left(13.78\right)=1.14 \\ 2\times 1.14=\mathrm{logx} \\ 2.28=\mathrm{logx} \\ \mathrm{x}=\mathrm{antilog}\left(2.28\right) \\ \mathrm{x}=190.54 \\ \mathrm{let} , {\left(0.968\right)}^3=\mathrm{y} \\ \mathrm{taking} \log \mathrm{both} \mathrm{sides}, \\ 3\log \left(0.968\right)=\mathrm{logy} \\ 3\left(-0.014\right)=\mathrm{logy} \\ \mathrm{y}=\mathrm{antilog}\left(-0.04\right)=1.10 \\ \sqrt[3]{\mathrm{x}+\mathrm{y}}=\sqrt[3]{190.54+1.10}=\sqrt[3]{191.64} \\ \mathrm{let} \sqrt[3]{191.64}=\mathrm{z} \\ \mathrm{taking} \log \mathrm{both} \mathrm{sides} \\ \frac{1}{3}\log \left(191.64\right)=\mathrm{logz} \\ \mathrm{from} \log \mathrm{table}, \log \left(191.64\right)=2.28 \\ \frac{2.28}{3}=\mathrm{logz} \\ 0.706=\mathrm{logz} \\ \mathbf{z}\mathbf{=}\mathbf{antilog}\left(\mathbf{0}\mathbf{.}\mathbf{706}\right)\mathbf{=}\mathbf{5}\mathbf{.}\mathbf{758} \end{gathered}$$

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