A Neat Little Parlour Trick

Yes, India has contributed more to maths than just the concept of 0 and the Decimal Number System

So there’s a bunch of really ancient Hindu scriptures known as the Vedas of which the oldest is the Rig-Veda one of foundations of Hinduism – open to lots and lots and lots of debate as it is apparently approximately 3500 years old….
Anyway, one of them apparently has a section on Maths… I was taught some of the stuff they call Vedic Mathematics in preparation for the entrance test for Indian Institute of Management. Anyway, I list below one of its secrets, for easy reference, which shall be updated, as when all of it comes back to me.

How to find the square of all numbers from 1 – 100

Ok so the square of numbers from 1-thru 13 most people have memorized, so I won’t mention them.
The square of all multiples of 10 (i.e. 10, 20, 30, 40) are easy to determine, so they don’t need to be covered either.

So here’s the neat trick. Vedic Mathematics gives you a cool way to figure out the square of any number ending in 5 (5, 15, 25, 35, e.t.c.).

Ok so let’s take the square of 95.
Every number that ends in 5, has a square that ends in 25.
So we know that the LAST TWO digits of 95-squared are 25.

How about the rest?
Well you take the digit(s) to left of the 5 (In this case 9) and multiply them by the next integer.
The only digit to the left of 5 is 9 in 95, so you multiply 9 by 9+1(10) to get 90.
Place the 90 to the left of 25 and you have your answer.

95 x 95 = 9025

Don’t believe me? Let’s try 65.
Last two digits of 65-squared are 25.
The rest of the result is found by multiplying 6 and 7(6+1) = 42

65 x 65 = 4225

The square of 105?
11025 (again, last digits are 25, and 10 x 11 gives u everything to the left)

Ok so great. Now we’ve got all the squares of multiples of 5, 10, and everything from 1 thru 13. Now to fill in the gaps. Here’s the final magic formula, which u may already know from your regualr algebra classes.

x+1 squared is = x squared + 2x + 1.

So that means that 36-squared is = 1225 + 71 = 1296
37-squared = 1296 + 73 = 1369
39-squared = 1600 – 40-39 = 1521 (going backwards from 40-squared, coz it’s easier)

and so on.

Well that ends the show for today. I’ve just touched very briefly on the subject there are lots of more interesting things you can do with Vedic Maths
So go on and wow your friends, show them that you’re secretly a math prodigy. :-p

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