Question

Find the cube root of $1331$ by the prime factorization method.

Answer 1

Apply prime factorization and calculate cube root

The given number is $1331$.

The prime factors of $1331$ can be calculated as,

So, $1331=11\times 11\times 11$

Then, the cube root of $1331$ is,

$$\begin{gathered} \sqrt[3]{1331}=\sqrt[3]{11\times 11\times 11} \\ \Rightarrow \sqrt[3]{1331}=11 \end{gathered}$$

Hence, the cube root of $1331$ is $11$.