1) Check whether 46656 is perfect cube
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Factors 2 × 2 and 5 × 5 are not in triples. ∴ 100 is not a perfect cube. Grouping the prime factors of 46656 in triples we are not left over with any prime factor. ∴ 46656 is a perfect cube.
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Therefore, 46656 is not a perfect cube because the last pair of 3 dosen't consist in triplets.
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