Find the cube root of 1728 by using the prime factorisation method.

To find the cube root we will do the prime factorization of 1728.

$1728=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3$

Taking cube root on both sides, we get:

$\sqrt[3]{1728}=\sqrt[3]{(2\times 2\times 2)\times (2\times 2\times 2)\times (3\times 3\times 3)}$

$=2\times 2\times 3$

$=12$

Hence the cube root of 1728 is 12.