Find the least number which must be added to 12864 to make it a perfect square

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.

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