Question

What is the following quotient?

Answer 1

First option is the correct answer.

`\huge{ \purple {2( \sqrt[3]{3} ) - \sqrt[3]{18} }}`

Explanation:

`\frac{6 - 3(\sqrt[3]{6} )}{ \sqrt[3]{9} } \\ \\ = \frac{ \sqrt[3]{ {6}^(3) } - \sqrt[3]{ {3}^(3) } . \sqrt[3]{6} }{ \sqrt[3]{9} } \\ \\ = \frac{ \sqrt[3]{216} - \sqrt[3]{ {3}^(3) * 6} }{ \sqrt[3]{9} } \\ \\ = \frac{ \sqrt[3]{216} - \sqrt[3]{ 27 * 6} }{ \sqrt[3]{9} } \\ \\ = \sqrt[3]{ (216)/(9) } - \sqrt[3]{ (27 * 6)/(9) } \\ \\ = \sqrt[3]{24} - \sqrt[3]{3 * 6} \\ \\ = \sqrt[3]{ {2}^(3) * 3} - \sqrt[3]{18} \\ \\ \huge{ \red{ = 2( \sqrt[3]{3} ) - \sqrt[3]{18} }}`