Question

Find the cube root by prime factorization $17576$

Answer 1

Find the cube root of given number using prime factorisation

Given, $17576$

$$\begin{gathered} \begin{array}{cc}2& 17576\\ 2& 8788\\ 2& 4394\\ 13& 2197\\ 13& 169\\ 13& 13\\ & 1\end{array} \\ \Rightarrow 17576=2^3·{13}^3 \\ \Rightarrow 17576={(2·13)}^3\Rightarrow 17576={26}^3 \\ \Rightarrow \sqrt[3]{17576}=26 \end{gathered}$$

Therefore, the cube root of $17576$ is $26$