Question

Find the cube root of the following number by prime factorization method: $91125$.

• A. $45$
• B. $35$
• C. $55$
• D. $465$

Answer 1

The correct option is A $45$

On prime factorising, we get,

$91125=(5\times 5\times 5)\times (3\times 3\times 3)\times (3\times 3\times 3)$

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

Then, cube root of $91125$ is:

$\sqrt[3]{391125}=\sqrt[3]{35^3\times 3^3\times 3^3}=5\times 3\times 3=45$.

Therefore, option $A$ is correct.