Question

Find the cube root by prime factorization of $10648$

Answer 1

Find cube root of given number using prime factorisation

Given, $10648$

$$\begin{gathered} \begin{array}{cc}2& 10648\\ 2& 5324\\ 2& 2662\\ 11& 1331\\ 11& 121\\ 11& 11\\ & 1\end{array} \\ \Rightarrow 10648=2^3·{11}^3 \\ \Rightarrow 10648={(2·11)}^3 \\ \Rightarrow 10648={22}^3 \\ \Rightarrow \sqrt[3]{10648}=22 \end{gathered}$$

Therefore, the cube root of $10648$ is $22$