Question

Find the cube root of 686/
-3456

Answer 1

Answer :

value of $\sqrt[3]{\frac{686}{-3456}}$

So,

$$\begin{gathered} \Rightarrow \sqrt[3]{\frac{2\times 7\times 7\times 7}{-2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3}} \\ \Rightarrow \sqrt[3]{\frac{2\times 7^3}{-2\times 2^3\times 2^3\times 3^3}} \\ \Rightarrow \frac{7}{2\times 2\times 3}\sqrt[3]{\frac{2}{-2}} \\ \Rightarrow \frac{7}{12}\sqrt[3]{-1} \\ \Rightarrow \frac{7}{12}\sqrt[3]{-1\times -1\times -1} \\ \Rightarrow \frac{7}{12}\sqrt[3]{{\left(-1\right)}^3} \\ \mathbf{\Rightarrow }\mathbf{-}\frac{\mathbf{7}}{\mathbf{12}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{(}\mathbf{}\mathbf{Ans}\mathbf{}\mathbf{)} \end{gathered}$$