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It is true that the square root of a Prime number like 11 is never a whole number. But to say that that has never been proven is incorrect. The square root of any positive integer that is not a square number (the square of an integer) is always irrational, and that is relatively easy to prove. To prove that prime numbers are not square numbers is even easier. That is basically true by definition. If a number greater than 1 were a square number, its square root would be a factor other than 1 and itself; therefore, it would not be a prime number.

Answer 1

No - the square root of 11 is not a whole number. 11 is prime so it has no factors except itself and 1, anyways.

Any prime number has no square root that is a whole number or integer. (That postulate has not been proven, but it has not been disproven so it is accepted as true.)

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Q: Is the square root of 11 a whole number?
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