The square root of 4725 is irrational!
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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.
Because square numbers have more than two factors whereas prime numbers have only two factors
Prime numbers only have two factors; square numbers (other than 1) have more than two.
All square numbers greater than 1 are composite.
No. To be prime it has to be divisible only by itself and one. That means that no numbers multiply to be it. The only possible exception is one. In the math world it may have been decided whether or not one is a prime number, but that is debatable and I'm not aware of the answer. If 1 was considered a prime number, then it would be the only prime square.