Question

Find the cube root of $512$ by the prime factorization method.

Answer 1

Evaluate the Cube Root:

The given number is $512$.

After resolving the prime factors, we get

$512=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$

Upon grouping the factors we get

$512=(2\times 2\times 2)\times (2\times 2\times 2)\times (2\times 2\times 2)$

Taking one factor from each group

$\sqrt[3]{512}=2x2x2$

$=8$

Hence, the required cube root is $8$.