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No, there are no prime numbers that are also square numbers. Prime numbers are only divisible by 1 and themselves, while square numbers have integer square roots. Since the square root of a prime number is not an integer, a prime number cannot be a square number.
No. For example, the square roots of prime numbers cannot be simplified.
All whole numbers between 1 and 400 (=20 square).
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Prime numbers can't have whole number square roots, of course, but the largest prime number under 400 is 397.