Question

How to find the cube root $74088$ with the prime factorization method.

Answer 1

Find the required cube root:

Split $74088$ into prime factors.

$$\begin{gathered} 74088=2\times 2\times 2\times 3\times 3\times 3\times 7\times 7\times 7 \\ 74088=2^3\times 3^3\times 7^3 \\ 74088=8\times 27\times 343 \\ \sqrt[3]{74088}=\sqrt[3]{8}\times \sqrt[3]{27}\times \sqrt[3]{343} \\ \sqrt[3]{74088}=2\times 3\times 7 \\ \sqrt[3]{74088}=42 \end{gathered}$$

Therefore cube root of $74088$ is $42$.