Question

find the cube root of the no 110592 by prime factorisation method

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{given}\mathrm{number}\mathrm{is}110592. \\ \mathrm{The}\mathrm{prime}\mathrm{factorisation}\mathrm{of}110592\mathrm{is} \\ 110592=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3 \\ \Rightarrow \sqrt[3]{110592}=\sqrt[3]{2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3} \\ \Rightarrow \sqrt[3]{110592}=2\times 2\times 2\times 2\times 3 \\ \Rightarrow \sqrt[3]{110592}=48 \end{gathered}$$