Question

Find the cube root of $27000$ by the prime factorization method.

Answer 1

Evaluate the Cube Root:

The given number is $27000$.

After resolving the prime factors, we get

$27000=2\times 2\times 2\times 3\times 3\times 3\times 5\times 5\times 5$

Upon grouping the factors we get

$27000=(2\times 2\times 2)\times (3\times 3\times 3)\times (5\times 5\times 5)$

Taking one factor from each group

$\sqrt[3]{27000}=2\times 3\times 5$

$=30$

Hence, the required cube root is $30$.