No.
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Nice question! The square root of (any number that isn't a perfect square) is irrational. No prime number is a perfect square. So the square root of any prime number is irrational.
True. By definition, a prime number is divisible by one and by itself. Also by definition, a perfect square has at least an additional pair of factors - it's square root. Therefore a prime number could never be a perfect square. One exception that might come to mind in this case is the number one. One however, is not considered a prime number, and thus does not conflict with this rule.
That is correct.
a perfect square
11 + 12 + 9 = 32