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Question

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


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Solution

Evaluate the Cube Root:

The given number is 32768.

After resolving the prime factors, we get

32768=2×2×2×2×2×2×2×2×2×2×2×2×2×2×2

Upon grouping the factors we get

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

Taking one factor from each group

327683=2x2x2x2x2

=32

Hence, the required cube root is 32.


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