Question

The value of $\sqrt[3]{3\sqrt[2]{20.000729}}$ is ______.

• A. 0.09
• B. 0.003
• C. 0.03
• D. 0.3

Answer 1

The correct option is D

0.3

First we evaluate the square root , we have

$\sqrt[2]{20.000729}$ = $\sqrt[2]{2\frac{729}{1000000}}$ = $\sqrt[2]{2\frac{27\times 27}{1000\times 1000}}$

= $\frac{27}{1000}$ = 0.027

Now expression $\sqrt[3]{3\sqrt[2]{20.000729}}$ deduce to,

$\sqrt[3]{30.027}$ = $\sqrt[3]{3\frac{27}{1000}}$ = $\sqrt[3]{3\frac{3\times 3\times 3}{10\times 10\times 10}}$

$\frac{3}{10}$ = 0.3

Hence $\sqrt[3]{3\sqrt[2]{20.000729}}=0.3$.