Evaluate the following:$\sqrt[3]{\left(\sqrt{0.000729}\right)} \ +\ \sqrt[3]{0.008}$

Given: $\sqrt[3]{\left(\sqrt{0.000729}\right)} \ +\ \sqrt[3]{0.008}$

To find: Here in this case we have to find the value of $\sqrt[3]{\left(\sqrt{0.000729}\right)} \ +\ \sqrt[3]{0.008}$

Solution:

$\sqrt[3]{\left(\sqrt{0.000729}\right)} \ +\ \sqrt[3]{0.008}$

$=\ \sqrt[3]{\left(\sqrt{\frac{729}{1000000}}\right)} \ +\ \sqrt[3]{\frac{8}{1000}}$

$=\ \sqrt[3]{\left(\sqrt{\frac{27^{2}}{1000^{2}}}\right)} \ +\ \sqrt[3]{\frac{2^{3}}{10^{3}}}$

$=\ \sqrt[3]{\frac{27}{1000}} \ +\ \frac{2}{10}$

$=\ \sqrt[3]{\frac{3^{3}}{10^{3}}} \ +\ \frac{2}{10}$

$=\ \frac{3}{10} \ +\ \frac{2}{10}$

$=\ \frac{5}{10}$

$=$ 0.5

So, value of the given expression is 0.5.

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Updated on: 10-Oct-2022

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