Question

Evaluate of the following

\[\sqrt[3]{27} + \sqrt[3]{0 . 008} + \sqrt[3]{0 . 064}\]

 

Answer 1

To evaluate the value of the given expression, we need to proceed as follows: 

\[\sqrt[3]{27} + \sqrt[3]{0 . 008} + \sqrt[3]{0 . 064} = \sqrt[3]{3 \times 3 \times 3} + \sqrt[3]{\frac{8}{1000}} + \sqrt[3]{\frac{64}{1000}}\]

\[= \sqrt[3]{3 \times 3 \times 3} + \frac{\sqrt[3]{8}}{\sqrt[3]{1000}} + \frac{\sqrt[3]{64}}{\sqrt[3]{1000}}\]

\[= \sqrt[3]{3 \times 3 \times 3} + \frac{\sqrt[3]{2 \times 2 \times 2}}{\sqrt[3]{1000}} + \frac{\sqrt[3]{4 \times 4 \times 4}}{\sqrt[3]{1000}}\]

\[ = 3 + \frac{2}{10} + \frac{4}{10}\]

\[ = 3 + 0 . 2 + 0 . 4\]

\[ = 3 . 6\]

Thus, the answer is 3.6.