This technique will help you to calculate Square of any two digit number in a quick way :
You might have to work with numbers some time and Squaring is the integral part of it . In professional life these tricks help in faster number crunching. Or if you are preparing for some entrance exams who require that you calculate fast : (In India, We have an MBA entrance exam called CAT,which requires such fast calculations and is one of the toughest exams in world because of immense competition).Or simply, If you want to impress your friends with some fast calculations , this technique would fit the bill.
This is how the technique works
(Only requirement is that you should know the squares of 1 to 25 at your fingertips)
First we classify the number X according to following condition
Group.1.: 25<= X<=50
Group.2. : 51<=X<=75
Group.3. : 76<=X<=100
For Group 1:
To find the square of X we do the following
- Find the Distance of X from 50 : distance Y = 50 -X
- Subtract the distance from 25 : result =25-Y
- Append two 0s to the result
- Add the square of the distance Y to the result (Here Y will be between 1 and 25 and you get the square of your number X !!
Looks complicated?
Well it wont when you see an example and do some practice .You will be able to calculate the squares in few seconds .
Example :(Group1)
Say you have to find the square of 41.
so X=41
- Find the distance of X from 50 : distance Y = 50 -41 =9
- Subtract the distance from 25 : result = 25-Y = 25-9 = 16
- Append two 0s to the result : result = 1600
- Add the square of the distance Y to the result : result = 1600 + 9^2 = 1600+81= 1681
so you get the square of 41 as 1681 . Just 4 steps to follow
For Group 2:
Now calculation for Group2 is almost same as that of Group1 : the only difference is that , rather than subtracting the distance from 25 we have to add it.
Example:(Group 2)
Say you have to find the square of 63.
so X=63
- Find the distance of X from 50 : distance Y = 63-50 =13
- Add the distance to 25 : result = 25 + Y = 25+13 = 38
- Append two 0s to the result : result = 3800
- Add the square of the distance Y to the result : result = 3800 + 13^2 = 3800+169= 3969
so you get the square of 63 as 3969 .
For Group 3:
Group 3 is somewhat different : Here we will calculate the distance from 100 and instead of subtracting from 25 (as we did in group 1 ), we will subtract from the X itself
Example:(Group 3)
Say you have to find the square of 94.
so X=94
- Find the distance of X from 100 : distance Y = 100-94 =6
- Subtract the distance from the X itself : result = X - Y = 94 - 6 = 88
- Append two 0s to the result : result = 8800
- Add the square of the distance Y to the result : result = 8800 + 6^2 = 8800+36= 8836
so you get the square of 94 as 8836 .
(There is a mathematical proof of this technique but I think its discussion would be irrelevant in this context . So send in your queries if you want to know the mathematical proof.)
