1. Which of the following numbers are not perfect cubes?
(1) 216
(m) 128
1000
(v) 46656
(iv) 100
Answers
(iv)I think 100 is answer.
Answer:
(i) We have 216 = 2 × 2 × 2 × 3 × 3 × 3
Grouping the prime factors of 216 into triples, no factor is left over.
∴ 216 is a perfect cube.
(ii) We have 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 Grouping the prime factors of 128 into triples, we are left over with 2 as ungrouped factor.
∴ 128 is not a perfect cube.
(iii) We have 1000 = 2 × 2 × 2 × 5 × 5 × 5 Grouping the prime factors of 1000 into triples, we are not left over with any factor.
∴ 1000 is a perfect cube.
(iv) We have 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.
(v) 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.
∴ 46656 is a perfect cube.