Question

Find The Cube Root Of $15625$ Number By Prime Factorization Method

Answer 1

Finding the cube root of $15625$ by Prime Factorization.

Prime factor of $15625=5\times 5\times 5\times 5\times 5\times 5$
$$\begin{gathered} =5^3\times 5^3 \\ ={(5\times 5)}^3 \\ ={\left(25\right)}^3 \end{gathered}$$
$$\begin{gathered} \Rightarrow \sqrt[3]{15625}=\sqrt[3]{{\left(25\right)}^3} \\ ={\left({25}^3\right)}^{\frac{1}{3}} \\ =25\left[\because {\left(a^n\right)}^m=a^{nm}\right] \end{gathered}$$

Hence, the cube root of $15625$ is $25$