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If the square root is a whole number, then the square of the square root, the original number, is also a whole number; all whole numbers can be expressed as themselves over 1, and so are rational numbers. The answer is thus any square number, ie the square of the natural numbers: 1 (1²), 4 (2²), 9 (3²), 16 (4²), etc.
Not sure what you mean by "perfect square root".A "perfect square" is the square of a whole number; if that's what you mean, yes, it's the square of the number 1.
No, a square root doesn't have to be a whole number. The square root of 2.25 is 1.5. It could be said that most square roots are not whole numbers. Take just the first few integers (counting numbers). Find the square roots of the numbers 1 through 10 and you'll find three of the numbers have whole number square roots (1, 4 and 9). The other seven don't. For the numbers 11 through 20, there is only 1 number with a whole number square root (16).
The square root of 49 is 7 which is a whole number but it can be expressed as 7/1 which is an improper fraction.
A perfect square is a number whose square root is a whole number, such as 1, 4, 9, 16, 25, etc.