Question

Find the cube root by prime factorization of $110592$

Answer 1

Find the cube root of given number using prime factorisation

Given, $110592$

$$\begin{gathered} \begin{array}{cc}2& 110592\\ 2& 55296\\ 2& 27648\\ 2& 13824\\ 2& 6912\\ 2& 3456\\ 2& 1728\\ 2& 864\\ 2& 432\\ 2& 216\\ 2& 108\\ 2& 54\\ 3& 27\\ 3& 9\\ 3& 3\\ & 1\end{array} \\ \Rightarrow 110592=2^{12}·3^3 \\ \Rightarrow 110592={(2^4·3)}^3 \\ \Rightarrow 110592={48}^3 \\ \Rightarrow \sqrt[3]{110592}=48 \end{gathered}$$

Therefore, the cube root of $110592$ is $48$