Find the cube root of 74088 by using the prime factorisation method.

To find the cube root we will do the prime factorization of 74088.

$74088=2\times 2\times 2\times 7\times 7\times 7\times 3\times 3\times 3$

Taking cube root on both sides, we get:

$\sqrt[3]{74088}=\sqrt[3]{(2\times 2\times 2)\times (7\times 7\times 7)\times (3\times 3\times 3)}$

$=2\times 7\times 3$

$=42$

Hence the cube root of 74088 is 42.