Question

Find the cube root of $91125$ by prime factorization method.

Answer 1

Apply prime factorization and calculate cube root

The given number is $91125$.

The prime factors of $91125$ can be calculated as,

$\begin{array}{cc}3& 91125\\ 3& 30375\\ 3& 10125\\ 3& 3375\\ 3& 1125\\ 3& 375\\ 5& 125\\ 5& 25\\ 5& 5\\ & 1\end{array}$

So, $91125=3\times 3\times 3\times 3\times 3\times 3\times 5\times 5\times 5$

Then, the cube root of $91125$ is,

$$\begin{gathered} \sqrt[3]{91125}=\sqrt[3]{3\times 3\times 3\times 3\times 3\times 3\times 5\times 5\times 5} \\ \Rightarrow \sqrt[3]{91125}=\sqrt[3]{\overline{3\times 3\times 3}\times \overline{3\times 3\times 3}\times \overline{5\times 5\times 5}} \\ \Rightarrow \sqrt[3]{91125}=3\times 3\times 5 \\ \Rightarrow \sqrt[3]{91125}=45 \end{gathered}$$

Hence, the cube root of $91125$ is $45$.