Question

Find \[\sqrt[3]{1.331}+\sqrt[3]{0.027}+\sqrt[3]{0.008}\]

Answer 1

Hint: The cubes of the given numbers are
\[\begin{align}
  & 1331={{11}^{3}} \\
 & 27={{3}^{3}} \\
 & 8={{2}^{3}} \\
\end{align}\]
Formulas used:
The cube root of any number,
\[\sqrt[3]{{{x}^{3}}}=x\].

Complete step-by-step answer:
First step will be calculating the cube of the given number,
The cube root of the given question is obtained.
The value can be obtained as,
\[\begin{align}
  & \sqrt[3]{1.331}+\sqrt[3]{0.027}+\sqrt[3]{0.008} \\
 & =\sqrt[3]{\left( \dfrac{1331}{1000} \right)}+\sqrt[3]{\left( \dfrac{27}{1000} \right)}+\sqrt[3]{\left( \dfrac{8}{1000} \right)} \\
 & =\sqrt[3]{{{\left( \dfrac{11}{10} \right)}^{3}}}+\sqrt[3]{{{\left( \dfrac{3}{10} \right)}^{3}}}+\sqrt[3]{{{\left( \dfrac{2}{10} \right)}^{3}}} \\
 & =\sqrt[3]{{{\left( 1.1 \right)}^{3}}}+\sqrt[3]{{{\left( 0.3 \right)}^{3}}}+\sqrt[3]{{{\left( 0.2 \right)}^{3}}} \\
 & =1.1+0.3+0.2 \\
 & =1.6 \\
\end{align}\]
Thus, the value of \[\sqrt[3]{1.331}+\sqrt[3]{0.027}+\sqrt[3]{0.008}\]is 1.6.

Note: The cube root of a number is a special value that, when used in a multiplication three times, gives that cube root of a number. The cube root of any number,
\[\sqrt[3]{{{x}^{3}}}=x\].