This is the solution sent in by Yatir Halevi. Thanks Yatir. A correct solution was also received from Andrei Lazanu.

Let's say we want to find the square of .

We know that

and for every a, we can pick a certain b that will make the calculation as easy as possible.

For instance if we take , we can take ,

we get

So, if is a number that ends with a 5: it can be written as

.

So is equal to q(q+1) plus two zeros after it that are "stolen" by the 25 that is added on.