Math, asked by curiousbrain540, 1 year ago

Findthe smallest number by which each of the following numbers must be multipled to obtain perfect square 243

Answers

Answered by ps5441158
5

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


Answered by BharghavADITYASHYAP
1
Ans:3
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