Question

Simplify the following expression:$\sqrt[3]{3\frac{729}{8}}-\frac{18}{\sqrt[3]{364}}$

• A. $0$
• B. $-9$
• C. $4.5
• D. $9$

Answer 1

The correct option is A $0$

$\text{Detailed step-by-step solution:}$
Given expression: $\sqrt[3]{3\frac{729}{8}}-\frac{18}{\sqrt[3]{364}}$

$=\frac{\sqrt[3]{3729}}{\sqrt[3]{38}}-\frac{18}{\sqrt[3]{364}}$ (writing $\sqrt[3]{3\frac{a}{b}}$ as $\frac{\sqrt[3]{3a}}{\sqrt[3]{3b}}$)

$=\frac{\sqrt[3]{39\times 9\times 9}}{\sqrt[3]{32\times 2\times 2}}-\frac{18}{\sqrt[3]{34\times 4\times 4}}$ (finding the factors of $729,8$, and $64$)

$=\frac{9}{2}-\frac{18}{4}$

$=\frac{9}{2}-\frac{9}{2}$ (simplifying $\frac{18}{4}$ to the simplest form as $\frac{9}{2}$)

$=0$

So, option D is the correct answer.