Question

Find the cube root of $46656$ by the prime factorization method.

Answer 1

Evaluate the Cube Root:

The given number is $46656$.

After resolving the prime factors, we get

$46656=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3\times 3\times 3\times 3$

Upon grouping the factors we get

$46656=(2\times 2\times 2)\times (2\times 2\times 2)\times (3\times 3\times 3)\times (3\times 3\times 3)$

Taking one factor from each group

$\sqrt[3]{46656}=2x2x3x3$

$=36$

Hence, the required cube root is $36$.