find the smallest number by which 25200 should be divided so that the result is a perfect square.

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Solution

$The given number is 25200 . Prime factorisation of 25200 is given by, 25200 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 5 \times 7 Since the prime factor 7, does not occur in pair, so the given number is not aperfect square . In order to make it a perfect square, we must divide it by 7 . So, required number = 7 .$

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find the smallest number by which 25200 should be divided so that the result is a perfect square.

The given number is 25200.Prime factorisation of 25200 is given by,25200 = 2×2×2×2×3×3×5×5×7Since the prime factor 7, does not occur in pair, so the given number is not aperfect square.In order to make it a perfect square, we must divide it by 7.So, required number = 7.