Concept 1: Square of ...5

As far as finding the square of any number ending with 5 is concerned there is a short-cut trick with which we can always find the square without putting much of an effort.

There is a mathematical relation between the digits of the square and the actual number. For finding out the square of the given number ending with 5, we first split the given number into 2 parts separating out the least significant digit (which always is 5) from the rest of the number and discarding it. In other words we simply remove the 5 at the end of the number.

For example if the given number is 45 we consider only 4 or if the given number is 125 we consider only 12.

Now we multiply the number so obtained by its succeeding number. In mathematical terms if the number obtained is ‘n’ we perform an operation and get the result x=n. (n+1)

We take this resultant number and attach a 25 at the end of it.

Hence the square of 45 will be equal to 4*5=2025 and that of 125 can be given as 12*13=15625.

You can check this trick out for any number ending with a 5 and you will always get an accurate result.