Question

Find the cube root of $15625$ by the prime factorization method.

Answer 1

Evaluate the Cube Root:

The given number is $15625$.

After resolving the prime factors, we get

$15625=5\times 5\times 5\times 5\times 5\times 5$

Upon grouping the factors we get

$15625=(5\times 5\times 5)\times (5\times 5\times 5)$

Taking one factor from each group

$\sqrt[3]{15625}=5\times 5$

$=25$

Hence, the required cube root is $25$.