Question

Find the cube root of $32768$ by the prime factorization method.

Answer 1

Evaluate the Cube Root:

The given number is $32768$.

After resolving the prime factors, we get

$32768=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$

Upon grouping the factors we get

$13824=(2x2x2)x(2x2x2)x(2x2x2)x(2x2x2)x(2x2x2)$

Taking one factor from each group

$\sqrt[3]{32768}=2x2x2x2x2$

$=32$

Hence, the required cube root is $32$.