Question

Q). Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.

(i) 243 - ___?
(ii) 256 - ___ ?​

Answer 1

Answer:

Prime factorizing 243, we get,

243=3×3×3×3×3=3

5

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We know, a perfect cube has multiples of 3 as powers of prime factors.

Here, number of 3's is 5.

So we need to multiply another 3 in the factorization to make 243 a perfect cube.

Hence, the smallest number by which 243 must be multiplied to obtain a perfect cube is 3.

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ii) 256 × 2 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) = 512 is a perfect cube. Hence, the smallest natural number by which 256 should be multiplied to make it a perfect cube is 2.

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Hi liza unnie!!

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Hope it helps you liza unnie!!

Borahae!! "