What square numbers add up to23?

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