Find the value of: $\sqrt[3]{0.008}+\sqrt[3]{5832}-\sqrt[3]{4.096}$.

Given: $\sqrt[3]{0.008}+\sqrt[3]{5832}-\sqrt[3]{4.096}$.

To do: To find the value of: $\sqrt[3]{0.008}+\sqrt[3]{5832}-\sqrt[3]{4.096}$.

Solution:

$\sqrt[3]{0.008}+\sqrt[3]{5832}-\sqrt[3]{4.096}$

$=\sqrt[3]{\frac{8}{1000}}+\sqrt[3]{5832}-\sqrt[3]{\frac{4096}{1000}}$

$=\sqrt[3]{\frac{2\times2\times2}{10\times10\times10}}+\sqrt[3]{18\times18\times18}+\sqrt[3]{\frac{16\times16\times16}{10\times10\times10}}$

$=\frac{2}{10}+18+\frac{16}{10}$

$=0.2+18+1.6$

$=19.8$

Therefore, $\sqrt[3]{0.008}+\sqrt[3]{5832}-\sqrt[3]{4.096}=19.8$

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Updated on: 10-Oct-2022

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