It does not matter! There are more numbers that are not perfect squares than there are perfect squares and the universe has not ground to a screeching halt!
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There is not a number that is a perfect square and perfect cube between 1 and 25.There is not a number that is a perfect square and perfect cube between 1 and 25.There is not a number that is a perfect square and perfect cube between 1 and 25.There is not a number that is a perfect square and perfect cube between 1 and 25.
"Still" implies that the original number is a square number. In that case, the answer is as follows: There is no number such that it is a perfect sqiuare and that the number increased (or decreased) by 10 is also a perfect square. And if you do not limit it to perfect square then every non-negative number is a square with the number that is 10 more also being a square.
Try taking the square root. If you get a whole number, then it is.
No.
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.