Question

1000 is a perfect cube??​

Answer 1

Question:-

• 1000 is a perfect cube?

Solution:-

⟶ Grouping the prime factors of 1000 into triples, we are not left over with any factor.

∴ 1000 is a perfect cube.

⟶ If We take 100 = 2 × 2 × 5 × 5

Grouping the prime factors into triples, we do not get any triples. Factors 2 × 2 and 5 × 5 are not in triples.

∴ 100 is not a perfect cube.

⟶ We have 46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3

Grouping the prime factors of 46656 in triples we are not left over with any prime factor.

Therefore:-

∴ 46656 is a perfect cube.

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