Question

PLEASE HELP

I posted the question below. Also I writing this part so it can exceed 20 characters xD

Answer 1

Hello!

So, this is quite the complex question, and here are the following steps:

What is the quotient of
`\frac{6-3\sqrt[3]{6}}{\sqrt[3]{9}}`?

`\frac{(6 - 3\sqrt[3]{6})\sqrt[3]{9^(2)}}{9}` (rationalize the denominator)

`\frac{3(2 -\sqrt[3]{6})\sqrt[3]{9^(2)}}{9}` (factor 3 from the expression)

`\frac{(2-\sqrt[3]{6})\sqrt[3]{9^(2)}}{3}` (reduce the fraction with 3)

`\frac{2\sqrt[3]{9^(2)}-\sqrt[3]{9^(2)}}{3}` (distributive property)

`\frac{2\sqrt[3]{81}-\sqrt[3]{486}}{3}` (simplify 3 · 9²)

`\frac{6\sqrt[3]{3}-3\sqrt[3]{18}}{3}` (simplify the radical)

`\frac{3(2\sqrt[3]{3}-3\sqrt[3]{18})}{3}` (factor 3 from the expression)

`2\sqrt[3]{3}-\sqrt[3]{18}` (reduce the fraction)

The answer, is simply, choice A,
`2\sqrt[3]{3} -\sqrt[3]{18}` ≈ 0.263758.