Question

Find the cube root of $175616$ by the prime factorization method.

Answer 1

Evaluate the Cube Root:

The given number is $175616$.

After resolving the prime factors, we get

$175616=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 7\times 7\times 7$

Upon grouping the factors we get

$175616=(2\times 2\times 2)\times (2\times 2\times 2)\times (2\times 2\times 2)\times (7\times 7\times 7)$

Taking one factor from each group

$\sqrt[3]{175616}=2x2x2x7$

$=56$

Hence, the required cube root is $56$.