Find the first perfect square that is larger than 12864. We can do this by taking the square root of 12864 finding the ceiling of that result and squaring it
which is
12996
Now find the difference between the next largest perfect square and the original number:
12996-12864
132
So 132 is the integer that needs to be added to 12864 to make it a perfect square.
Check:
Take the square root of 12864+132:
%:12864+132
114
So it’s a perfect square.