Evaluate the following:$\sqrt[3]{\sqrt{0.000729}}+\sqrt[3]{0.008}$

Given :

The given expression is $\sqrt[3]{\sqrt{0.000729}} +\sqrt[3]{0.008}$.

To do :

We have to evaluate the given expression.

Solution :

$\sqrt[3]{\sqrt{0.000729}} =\sqrt[3]{\sqrt{( 0.027)^{2}}}$

$=\sqrt[3]{( 0.027)^{2\times \frac{1}{2}}}$

$=\sqrt[3]{0.027}$

$=\sqrt{( 0.3)^{3}}$

$=( 0.3)^{3\times \frac{1}{3}}$

$=0.3$

$\sqrt[3]{0.008} =\sqrt[3]{( 0.2)^{3}}$

$=( 0.2)^{3\times \frac{1}{3}}$

$=0.2$

Therefore,

$\sqrt[3]{\sqrt{0.000729}} +\sqrt[3]{0.008} =0.3+0.2=0.5$.

The value of $\sqrt[3]{\sqrt{0.000729}} +\sqrt[3]{0.008}$ is 0.5.

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Updated on: 10-Oct-2022

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