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Find the smallest number by which 2560 must be multiplied so that the product is a perfect cube

Posted by Vansh Chawla 5 years, 6 months ago

CBSE > Class 08 > Mathematics

2 answers

Sneha Ramparia 5 years, 6 months ago

2560=2×2×2×2×2×2×2×2×2×5 =2 3 ×2 3 ×2 3 ×5. ∴2 3 ×2 3 ×2 3 ×5(5×5) is a perfect cube. So we should multiply 2560 by (5×5)=25 to make it a perfect cube.

0Thank You

Sneha Ramparia 5 years, 6 months ago

Smallest number to be multiplied is 5^{2}=25 Step-by-step explanation: Factorization is the process of simplifying the number based on its factors or divisors. Now, we need to find the smallest number by applying the factorization to the given number. Now, by factorizing the given number, we get, \therefore 2560=2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5=2^{9} \times 5 The nearest perfect cube is obtained by multiplying 2^{9} \text { and } 5^{3} Therefore, the nearest perfect cube of 2^{9} \times 5=2^{9} \times 5^{3} Hence, the smallest number to be multiplied is 5^{2}=25

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CBSE > Class 08 > Mathematics