Question

Evaluate: $\sqrt[3]{3\sqrt{0.000729}}+\sqrt[3]{30.008}$

Answer 1

Now,

$\sqrt[3]{3\sqrt{0.000729}}+\sqrt[3]{30.008}$

$=\sqrt[3]{3\sqrt{\frac{729}{{10}^6}}}+\sqrt[3]{3\frac{8}{{10}^3}}$

$=\sqrt[3]{3\sqrt{\frac{3^6}{{10}^6}}}+\sqrt[3]{3\frac{2^3}{{10}^3}}$

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

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

$=\frac{5}{10}$

$=\frac{1}{2}$.