Bonus for the weekend!

I thought of adding another small trick which is pretty helpful as the week comes to an end.This has also been a pretty useful trick but has an underlying assumption.The trick is about calculating square on a number given the square of the preceding or the succeeding number.The funda comes from a formula which most of us would have done as a start to algebra in class 6th.The formula is and I think all of you would remember it-

a^2-b^2=(a-b)(a+b)

For the uninitiated ^ implies the 'raised to the power of ' sign.

Funda-To calculate the square on a number without multiplying it by itself you can use the following technique if you have the square of the preceding number with you.

1)Add the 2 consecutive numbers

2)Add the sum to the square of the preceding number.

3)In this case the (a-b) term becomes 1 and that is what makes the difference of the squares the sum of the numbers.

Let me elucidate with an example.

Example-Let me calculate the square of 76 for you guys.I hope everyone knows the square of 75.If you dont you can learn this trick about calculating squares of numbers ending with 5(Believe me this is justs the tip of the iceberg).The square will always end with the last two digits as 25.The first few digits can be calculated by multiplying the number preceding 5(in this case 7) with the next number(in this case 7+1=8).The multiplication of 7 and 8 will give us 56 which become the first 2 digits of the square giving us the answer as 5625.

Now that we have the square of 75 we follow the steps mentioned

1)Add 75 and 76 to get 151

2)Add 151 to the square of 75 i.e. 5625

3)The sum i.e. 5776 is your answer

The underlying assumption that I mentioned before is that you should be quick enough with your additions and should know the squares of some important numbers atleast.

Hopefully you enjoyed this funda and can come back next week when I really start with some amazing revelations.Until then Happy Solving!