Find the cube root of 64000 by using the prime factorisation method.

To find the cube root we will do the prime factorization of 64000.

$64000=2\times 2\times 2\times 2\times 2\times 2\times 5\times 5\times 5\times 2\times 2\times 2$

Taking cube root on both sides, we get:

$\sqrt[3]{64000}=\sqrt[3]{(2\times 2\times 2)\times (2\times 2\times 2)\times (5\times 5\times 5)\times (2\times 2\times 2)}$

$=2\times 2\times 5\times 2$

$=40$

Hence the cube root of 64000 is 40.