I assume by "square numbers" you mean perfect squares.
You didn't say how many of each were allowed:
1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1²= 23
1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² = 23
1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² + 2² = 23
1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 3² = 23
1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² + 2² + 2² = 23
1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² + 3² = 23
1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² + 2² + 2² + 2² = 23
1² + 1² + 1² + 1² + 1² + 1² + 1² + 4² = 23
1² + 1² + 1² + 1² + 1² + 3² + 3² = 23
1² + 1² + 1² + 2² + 2² + 2² + 2² + 2²= 23
1² + 1² + 1² + 2² + 4² = 23
The two square numbers that add up to 225 are 144+81 = 225
The two square numbers which add up to 13 are 9 (which is equal to 3 squared), and 4 (which is equal to 2 squared).
16,25,36 add to 77. They are the squares of consecutive numbers 4,5,6
x2 = 45take square root of both sidesx = positive and negative square root of 45x = + and - 3√(5)Improved Answer:-9 and 36 are square numbers and they add up to 45
9 + 16 = 25
92
The two square numbers that add up to 225 are 144+81 = 225
67
The two square numbers which add up to 13 are 9 (which is equal to 3 squared), and 4 (which is equal to 2 squared).
16,25,36 add to 77. They are the squares of consecutive numbers 4,5,6
16 and 64
68
x2 = 45take square root of both sidesx = positive and negative square root of 45x = + and - 3√(5)Improved Answer:-9 and 36 are square numbers and they add up to 45
11664 and 36
16, 25
55
the two numbers in the circles add up to the number in the square box!