I'm not sure exactly what your question is, but the squares of 4 and 5 do have this property (and are the only perfect squares that do).
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The two square numbers would be 9 and 1 ( (3 x 3)-(1 x 1) )
subtract the lowest number from the highest number.
It is another rational number whose numerator and denominator (in the ratio's simplest form) are perfect squares.
In surd form, square roots need to be have the same radical term before you can add or subtract them. However, unlike in algebraic expressions, it is possible to add or subtract square roots using approximate (decimal) values.
subtract any number form nine and then with that answer and the number you subtracted 9 with, those added, make the sum of nine