Question

Find the cube root of $1728$ by the prime factorization method.

Answer 1

Evaluate the Cube Root:

The given number is $1728$.

After resolving the prime factors, we get

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

Upon grouping the factors we get

$1728=(2\times 2\times 2)\times (2\times 2\times 2)\times (3\times 3\times 3)$

Taking one factor from each group

$\sqrt[3]{1728}=2x2x3$

$=12$

Hence, the required cube root is $12$.