No
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Sure. Take the fourth power of any natural number, for example 24 = 16. It square root is a perfect square, in this case 22. As another example, the square root of 34 = 32.
No, 325 is not a perfect square however 324 is a perfect square.
38 is not a perfect square. Its square root is a fraction and the square root of a perfect square is always an integer.
No- the closest perfect squares are 36 (perfect square of 6) and 49 (perfect square of 7)
It is the square of an integer: that is what a perfect square is.