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Cube Roots

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Question

Find the cube root of $4096$ by the prime factorization method.

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Solution

Evaluate the Cube Root:
The given number is $4096$ .
After resolving the prime factors, we get
$4096 = 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2 X 2$
Upon grouping the factors we get
$4096 = (2 X 2 X 2) X (2 X 2 X 2) X (2 X 2 X 2) X (2 X 2 X 2)$
Taking one factor from each group
$\sqrt[3]{4096} = 2 x 2 x 2 x 2$
$= 16$
Hence, the required cube root is $16$ .

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