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I suspect you are talking about integers here, though you don't say so. These situations are called Pythagorean Triplets (In a triangle with 1 right-angle, the sum of the squares of the smaller sides equals the square of the longer side). The smallest (apart from 0,0 and 0) is 52 = 42 + 32. If you are not talking about integers then there is no limit on smallness (apart from 0,0,0).

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Q: What is the smallest square number that is a sum of two square number?
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