Question

Find the cube root $\sqrt[3]{\frac{343}{64}}$

Answer 1

Given: $\sqrt[3]{\frac{343}{64}}$

Since, $\frac{343}{64}=\frac{7}{4}\times \frac{7}{4}\times \frac{7}{4}={\left(\frac{7}{4}\right)}^3$.

Then,

$\sqrt[3]{\frac{343}{64}}=\sqrt[3]{{\left(\frac{7}{4}\right)}^3}=\frac{7}{4}$ ( $\because$ cancel cube with cube root )

Hence, $\sqrt[3]{\frac{343}{64}}=\frac{7}{4}$.