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).
25 (32 + 42 = 52)
The smallest three-digit square number is 100, which is (10^2). However, it cannot be expressed as the sum of two squares. The next three-digit square is 121 ((11^2)), which can be expressed as (11^2 = 10^2 + 1^2). Thus, 121 is the smallest three-digit square number that is also the sum of two squares.
25= 5*5 = (3*3)+(4*4)
16
16
25 (32 + 42 = 52)
The smallest three-digit square number is 100, which is (10^2). However, it cannot be expressed as the sum of two squares. The next three-digit square is 121 ((11^2)), which can be expressed as (11^2 = 10^2 + 1^2). Thus, 121 is the smallest three-digit square number that is also the sum of two squares.
25= 5*5 = (3*3)+(4*4)
Oh, dude, you're hitting me with some math riddles now? Alright, so the smallest square number that is the sum of two square numbers is 5, because 5 = 1^2 + 2^2. It's like a math puzzle for people who actually enjoy math, you know?
10^2 = 6^2 + 8^2 ie 100 = 36 + 64
5
16
16
The smallest two digit number is 00 (a number used as a wire gauge) and the biggest is 99, so the sum of the biggest and smallest 2-digits numbers is 99 (99 + 00).
12
1+2=3
The 3rd square number is (3^2 = 9) and the 5th square number is (5^2 = 25). The sum of these two square numbers is (9 + 25 = 34).