Question

Evaluate each of the following:

iii) $\sqrt[3]{3\frac{729}{216}}\times \frac{6}{9}$

Answer 1

Step: Evaluate $\sqrt[3]{3\frac{729}{216}}\times \frac{6}{9}$

$\sqrt[3]{3\frac{729}{216}}\times \frac{6}{9}=\frac{\sqrt[3]{3729}}{\sqrt[3]{3216}}\times \frac{6}{9}$

$[\because \sqrt[3]{3\frac{a}{b}}=\frac{\sqrt[3]{3a}}{\sqrt[3]{3b}}]$


$=\frac{\sqrt[3]{39\times 9\times 9}}{\sqrt[3]{36\times 6\times 6}}\times \frac{6}{9}$

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

$=1$

Hence, the value of $\sqrt[3]{3\frac{729}{216}}\times \frac{6}{9}$ is $1$