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Question

Find the cube root of 512 by the prime factorization method.


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Solution

Evaluate the Cube Root:

The given number is 512.

After resolving the prime factors, we get

512=2×2×2×2×2×2×2×2×2

Upon grouping the factors we get

512=(2×2×2)×(2×2×2)×(2×2×2)

Taking one factor from each group

5123=2x2x2

=8

Hence, the required cube root is 8.


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