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No 38 is not a square number.
When you square a real number the answer is positive,
"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.
The square of a negative number is always positive. The square of -8 = 64, a rational number
Any even number you square will give you a even square number =)