Question

Find the cube root of $12167$ by prime factors

Answer 1

Finding the cube roots of $12167$ by prime factorization.

Prime factor of $12167=23\times 23\times 23$
$$\begin{gathered} \Rightarrow \sqrt[3]{12167}=\sqrt[3]{{23}^3} \\ ={\left({23}^3\right)}^{\frac{1}{3}} \\ =23\left[\because {\left(a^m\right)}^n=a^{mn}\right] \end{gathered}$$

Hence, the cube root of $12167$ is $23$