Find the cube root of $438976$ by the prime factorization method.

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Solution

Evaluate the Cube Root:
The given number is $438976$ .
After resolving the prime factors, we get
$438976 = 2 x 2 x 2 x 2 x 2 x 2 x 19 x 19 x 19$
Upon grouping the factors we get
$438976 = (2 x 2 x 2) x (2 x 2 x 2) x (19 x 19 x 19)$
Taking one factor from each group
$\sqrt[3]{438976} = 2 x 2 x 19$
$= 76$
Hence, the required cube root is $76$ .

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