Question

Find the cube root of $64$ by prime factorization method.

Answer 1

Apply prime factorization and calculate cube root

The given number is $64$.

The prime factorization of $64$ can be calculated as,

$\begin{array}{cc}2& 64\\ 2& 32\\ 2& 16\\ 2& 8\\ 2& 4\\ 2& 2\\ & 1\end{array}$

So, $64=2\times 2\times 2\times 2\times 2\times 2$

Then, the cube root of $64$ is,

$$\begin{gathered} \sqrt[3]{64}=\sqrt[3]{2\times 2\times 2\times 2\times 2\times 2} \\ \Rightarrow \sqrt[3]{64}=\sqrt[3]{\overline{2\times 2\times 2}\times \overline{2\times 2\times 2}} \\ \Rightarrow \sqrt[3]{64}=2\times 2 \\ \Rightarrow \sqrt[3]{64}=4 \end{gathered}$$

Hence, the cube root of $64$ is $4$.