When it can be square rooted
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Assuming your number is an integer: if the number is a perfect square, the number is of course an integer, and therefore rational. If the number is NOT a perfect square, it is irrational.
If by 'perfect number' you mean 'perfect SQUARE', then yes. 49 is an odd number and a perfect square.
If you have a number like 12 and you multiply it by the same number: 12 and the answer you get is a whole number, then the whole number is the perfect square.
A number is a perfect square when you can directly extract its square root in whole numbers and without approximation. When you subject a certain number to a radical sign, you can extract its square. Example: 25 is a perfect square. it's square root is 5, since 5 x 5 is equal to 25
You take the square root of the number. If it is a perfect square, this will be a whole number. If it is not, it isn't a perfect square.