Question

Find the cubic root of the following number by prime factorisation method:

$27000$

Answer 1

On prime factorising, we get,

$27000=2\times 2\times 2\times 5\times 5\times 5\times 3\times 3\times 3$

$=2^3\times 5^3\times 3^3$.

Then, cube root of $27000$ is:

$\sqrt[3]{327000}=\sqrt[3]{33^3\times 5^3\times 2^3}=3\times 5\times 2=30$.

Therefore, $30$ is the required solution.