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Numbers that can go into both 90 and 144 are 1, 2, 3, 6, 9, and 18.
144 has only one square, and that is 20,736.
The subsets of all the square roots of 144 are {+12} and {-12}. The single set that includes all the square roots of 144 is {+12, -12}. That's all there are. There are no more.
How about: 100+44 = 144 or 12*12 = 144
12*12, 6*24, 3*48, ect.