Question

Find the cube root of $729$ by the prime factorization method.

Answer 1

Apply prime factorization and calculate cube root

The given number is $729$.

The prime factors of $729$ can be calculated as,

So, $729=3\times 3\times 3\times 3\times 3\times 3$

Then, the cube root of $729$ is,

$$\begin{gathered} \sqrt[3]{729}=\sqrt[3]{3\times 3\times 3\times 3\times 3\times 3} \\ \Rightarrow \sqrt[3]{729}=\sqrt[3]{\overline{3\times 3\times 3}\times \overline{3\times 3\times 3}} \\ \Rightarrow \sqrt[3]{729}=3\times 3 \\ \Rightarrow \sqrt[3]{729}=9 \end{gathered}$$

Hence, the cube root of $729$ is $9$.