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One can judge just by look, that the each of the following numbers (82, 113, 2057, 24353, 8888,1972) is not a perfect square. Explain why?

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Because the unit digit of a perfect square will be 0, 1, 4, 5, 6, 9. But the given numbers have unit digits 2, 3, 7, 8. So they are not perfect squares.

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