Question

Find $\sqrt[3]{3\frac{7290\times 20\times 5}{343\times 216}}$

• A. $1\frac{1}{7}$
• B. $2\frac{1}{7}$
• C. $3\frac{1}{7}$
• D. $3\frac{1}{8}$

Answer 1

The correct option is B

$2\frac{1}{7}$

$\sqrt[3]{3\frac{7290\times 20\times 5}{343\times 216}}$

= $\sqrt[3]{3\frac{729\times 10\times 20\times 5}{343\times 216}}$

= $\sqrt[3]{3\frac{729\times 1000}{343\times 216}}$

= $\frac{\sqrt[3]{3729}\times \sqrt[3]{31000}}{\sqrt[3]{3343}\times \sqrt[3]{3216}}$

We have $\sqrt[3]{3729}$ = 9 ; $\sqrt[3]{31000}$ = 10 ; $\sqrt[3]{3343}$ = 7 ; $\sqrt[3]{3216}$ = 6 ;

= $\frac{9\times 10}{7\times 6}$

= $\frac{90}{42}$

= $\frac{15}{7}$

= $2\frac{1}{7}$