Question

PLEASE HELP

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.