Question

What is the following quotient? 6-3(3 √8)/3 √9

Answer 1

The correct option is A)
`2\sqrt[3]{3}-{\sqrt[3]{18}`

Explanation:

Consider the provided expression.

`\frac{\left(6-3\left(\sqrt[3]{6}\right)\right)}{\sqrt[3]{9}}`

Rationalize by multiplying conjugate
`\frac{9^{(2)/(3)}}{9^{(2)/(3)}}`

`\frac{\left(6-3\sqrt[3]{6}\right)\cdot \:9^{(2)/(3)}}{\sqrt[3]{9}\cdot \:9^{(2)/(3)}}`

`\frac{9^{(2)/(3)}\cdot \:3\left(2-\sqrt[3]{6}\right)}{9}`

`\frac{9^{(2)/(3)}\left(2-\sqrt[3]{6}\right)}{3}`

`\frac{3^{(4)/(3)}\left(2-\sqrt[3]{6}\right)}{3}`

`3^{(1)/(3)}\left(2-\sqrt[3]{6}\right)`

`2\sqrt[3]{3}-3^{(2)/(3)}\sqrt[3]{2}`

`2\sqrt[3]{3}-{\sqrt[3]{18}`

Hence, the correct option is A)
`2\sqrt[3]{3}-{\sqrt[3]{18}`