Findthe smallest number by which each of the following numbers must be multipled to obtain perfect square 243
Answers
Answer:
Step-by-step explanation:Sol. (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
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