Question

Find the cube root of $6859$ by prime factorization method.

Answer 1

Apply prime factorization and calculate cube root

The given number is $6859$.

The prime factorization of $6859$ can be calculated as,

$\begin{array}{cl}19& 6859\\ 19& 361\\ 19& 19\\ & 1\end{array}$

So, $6859=19\times 19\times 19$

Then, the cube root of $6859$ is,

$$\begin{gathered} \sqrt[3]{6859}=\sqrt[3]{19\times 19\times 19} \\ \Rightarrow \sqrt[3]{6859}=19 \end{gathered}$$

Hence, the cube root of $6859$ is $19$.