How To Find Square Of Number Ending In Digit 5?

Can we calculate 65x65 in fraction of seconds? Answer is yes and here I am presenting a trick.

The last two digit of your answer will always be 25. In order to find rest of the digits Multiply the number without unit digit `5` with next whole number.

i.e in case of 65x65, last two digit will be 25. To find rest of the digit take the number without unit digit `5`, i.e. 6. Multiply it with its next whole number i.e. 7. That is 6*7= 42. Hence answer will be 65x65=4225. Check it :)

Now try others 75x75=5625 [7*(7+1)=56 combined with 25] 45x45=2025 [4*(4+1)=20 combined with 25]

So the question is why is it working? Any number with last digit "5" can be written as 10*x + 5.

So if we square (10*x + 5)*(10*x + 5) = 100*x*x + 50*x + 50*x + 25 = 100*x*x + 100*x + 25 = 100*x(x+1) + 25

Due to 100, the result will always have 25 as last two digit. The other digits can be found as x*(x+1).

Good Luck !!!