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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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