Question

Find the cube root of $4096$ by the prime factorization method.

Answer 1

Evaluate the Cube Root:

The given number is $4096$.

After resolving the prime factors, we get

$4096=2X2X2X2X2X2X2X2X2X2X2X2$

Upon grouping the factors we get

$4096=(2X2X2)X(2X2X2)X(2X2X2)X(2X2X2)$

Taking one factor from each group

$\sqrt[3]{4096}=2x2x2x2$

$=16$

Hence, the required cube root is $16$.