Question

Evaluate of the following

\[\sqrt[3]{1000} + \sqrt[3]{0 . 008} - \sqrt[3]{0 . 125}\]

Answer 1

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

\[\sqrt[3]{1000} + \sqrt[3]{0 . 008} - \sqrt[3]{0 . 125} = \sqrt[3]{10 \times 10 \times 10} + \sqrt[3]{\frac{8}{1000}} - \sqrt[3]{\frac{125}{1000}}\]

\[= \sqrt[3]{10 \times 10 \times 10} + \frac{\sqrt[3]{8}}{\sqrt[3]{1000}} - \frac{\sqrt[3]{125}}{\sqrt[3]{1000}}\]

\[= \sqrt[3]{10 \times 10 \times 10} + \frac{\sqrt[3]{2^3}}{\sqrt[3]{1000}} - \frac{\sqrt[3]{5^3}}{\sqrt[3]{1000}}\]

\[ = 10 + \frac{2}{10} - \frac{5}{10}\]

\[ = 10 + 0 . 2 - 0 . 5\]

\[ = 9 . 7\]

Thus, the answer is 9.7.