Quantitative Aptitude: Shortcut trick for Finding Squares using Vedic Maths

Hello Readers,

Today we are sharing a Vedic Method for finding the Squares of any given number. This method is called "Vedic Nikhilam Method" and is found in Atharva Veda. In this post, we are introducing the method for finding the Squares of numbers closer to 100, 1000, 10000, etc in very speedy manner.

Method

(1) Find out the square of 99 or 99^2 
Sol- 
Step - 1: Find the Base

• Base is a power of 10 nearest to given number. In this example, 100 is the nearest number to 99. So we will take 100 as our base.

Step -2 : Find the Deviation from the Base

• Deviation from base 100-99=01

Step -3 : Finding the Square: We can directly write the answer in Two Parts one after another-

Part A   Part B

• Part A : It is a number obtained from subtracting deviation from the given number. Part A = 99-1= 98
• Part B : It is a two digit number(for base 100, 3 digit number for base 1000 and so on..) and can be obtained by squaring the deviation. So, Part B = (01)²= 01

So, (99)² = 9801

2. Finding out the Square of (102)² : When the number is more than base, the deviation to be added to the number to get Part A.

Part A : Deviation=102-100=2

Part B : (02)²=04

So, (102)²=10404

	Number	Base	Deviation	Part A	Part B	Answer
c)	(94)2	100	100-94=6	94-6=88	62=36	8836
d)	(92) 2	100	100-92=8	92-8=84	82=64	8464
e)	(104)2	100	104-100=04	104+4=108	42=16	10816
f)	(994)2	1000	1000-994=6	994-6=988	62=036	988036
g)	(992)2	1000	1000-992=8	992-8=984	82=064	984064
h)	(9992)2	10000	10000-9992=8	9992-8=9984	82=0064	99840064
i)	(1006)2	1000	1006-1000=6	1006+6=1012	62=036	1012036

By regular practicing this method, one can easily find out square of nearest number of 10, 100, 1000, 1000 and so on.

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