Question

Solve $\sqrt[3]{3\frac{-125}{343}}$

Answer 1

Consider $\sqrt[3]{3\frac{-125}{343}}$

Using $\sqrt[n]{n-a}=-\sqrt[n]{na}$ (if $n$ is odd) we get

$\sqrt[3]{3\frac{-125}{343}}=-\sqrt[3]{3\frac{125}{343}}$

$=-\frac{\sqrt[3]{3125}}{\sqrt[3]{3343}}$

$=-\frac{5}{7}$

$\sqrt[3]{3\frac{-125}{343}}=-\frac{5}{7}$