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Because its square root is an irrational number that can't be expressed as a fraction.

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The closest perfect squares are 31^2 = 961, and 32^2 = 1024.

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If you simplify, sqrt(1000) = sqrt(100) * sqrt(10) = 10 * sqrt(2) * sqrt(5). 2 and 5 are prime numbers so there is no way to ever get rid of the radical.

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Q: Why is 1000 not a perfect square?
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