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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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Earn +20 ptsQ: Why is 1000 not a perfect square?
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Is 1000 a perfect square explain?
1,000 is a not perfect square.
Is 1000 a perfect square?
No
What is the first perfect square after 1000?
1024
What is the largest perfect square less than 1000?
312 = 961
Why is the square root of 1000 an irrational number?
The square root of any non-perfect square is an irrational number. Since sqrt(1000) = 10 sqrt(10), it is irrational.
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