Question

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

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Solution

2560 2560 can be expressed as the product of prime factors in the following manner: 2560 = $2×2×2×2×2×2×2×2×2×5$ To make this a perfect square, we have to multiply it by 5$×$5. Therefore, 2560 should be multiplied by 25 so that the product is a perfect cube.

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