Question

Find the cube root of 74088 by prime factorization.

Answer 1

$\text{Consider}74088.\text{We find its cube root by prime factorization.}74088=2\times 2\times 2\times 3\times 3\times 3\times 7\times 7\times 7=2^3\times 3^3\times 7^3$

$\sqrt[3]{374088}=\sqrt[3]{32^3\times 3^3\times 7^3}=\sqrt[3]{3{42}^3}=42$