Question

Find the cube root of $125$ number by prime factorization method.

Answer 1

Finding the cube root of $125$ by Prime Factorization.

Prime factor of $125=5\times 5\times 5$
$$\begin{gathered} \Rightarrow \sqrt[3]{125}=\sqrt[3]{5^3} \\ ={\left(5^3\right)}^{\frac{1}{3}} \\ =5\mathbf{}\left[\because {\left(a^n\right)}^m=a^{\mathrm{nm}}\right] \end{gathered}$$

Hence the cube root of $125$ is $5$