How to square numbers easy and fast using Vedic Mathematics?
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Master Formula to Calculate Square in 10 Seconds.
Square of numbers ending with 5
Formula for calculating square ending with 5 is easy. I have also discussed this multiplication in my multiplication Article.
85
x
85
-------------
7225
Steps
• Multiply 5 by 5 and put composite digit 25 on the right hand side.
• Add 1 to the upper left hand side digit i.e. 8 i.e. 8+1=9
• Multiply 9 to the lower hand digit 8, i.e. 9*8=72
• Our answer is 7225.
Using this method we can find out square of the number. Now let’s have a look at method of calculating square of adjacent number.
Forward Method
We know method to find square of a number ending with 5., say Square of 75=5625, then just have a look to find square of 76.
75’s square=5625(known)
76’square=75’square+ (75+76) =5625+151=5776.
So square of 76 is 5776.
Steps
• Steps are simple. The format shown above is self explanatory. But still I am explaining it.
• 75’square=5625 is known
• Add (75+76=151) to this to get 76’square
• 76’square=5776.
Reverse Method
As like forward method for calculating square of number which is 1 more than the given number whose square is known, we have reverse method to find square.
Now let me explain in detail the Reverse approach through which You will able to find out squares of a number which is one less than given number.
Consider the following example:
Suppose we know square of a number, say, 70; how to find square of 69?
(70)’square=4900(known)
(69)’square=4900-(69+70) =4900-139
=4761.
Mental formula for finding Squares
Let us first find square of 11 using formula:
11’square=11+1/1square=12/1=121.
The formula is self explanatory. However, let me explain it in detail for more clarification.
• The slash is used just as a operator.
• Our operating zone is 10 X 1 or simply 10.
• 11 is more than 10.
• We add 1 to 11to make 12.
• The number of digits after the slash can be only one.
• If the number of digits after the slash exceeds one, then we place only the rightmost digit on the extreme right after the slash, and the remaining gets added to the number on the left hand side of the slash.
• Now have a look at few more examples for better understanding.
12’square=12+2/2’square=14/4=144
13’square=13+3/3’square=16/9=169.
14’square=14+4/4’square=18/16 (Apply step no 6 here) 18/16=18+1/6=196.
15’square=15+5/5’square=20/25=20+2/5=225.
16’square=16+6/6’square=22/36=22+3/6=256.
You can work like this up to 19’square.But for 20 formula is slightly change.
The slight Change in formula as follows:
21’square=2 X (21+1)/1’square= 2 X (22)/1=44/1=441.
This change is because now we are operating in the 10 X 2 Zone. Similarly we can calculate Square of 31 but with slight change as follows:
31’Square=3 X (31+1)/!’square= 3 X (32)/1=96/1=961.
By these methods explained you can easily calculate and memorize the squares of numbers up to 99 with out much hassle.
Master Formula to Calculate Square in 10 Seconds.:
Till now we have seen various formulae to calculate square of the number. Now I am giving such a master Formula by which you can orally calculate Square of the number with in 10 Seconds.
11’square=121. 12’square=144
111’square=12321 121’square=14641
Steps:
• Consider number 121 to find square.
• Separate digits as 12 & 1.
• Now do Square of unit digit number i.e. 1’square=1, so our unit digit number is 1 now in this case.
• Then multiply both separated Digits which are earlier separated ie.12 & 1
• =12 X 1=12
• Now double the result of multiplication i.e. Double of 12= 24. And place it left after unit digit number i.e. 2 41.( 2 is Carry)
• Separate carry 2 then
• Now At last square 12 i.e. 12’square=144 and add earlier Carry to it.
• So we get 144+2(carry)=146
• Finally we obtained Square as 14641..
Let us have a look at one more example.
151’square:
• 1’s square=1.
• 2 x (15 x 1) = 3 0 (Double of 15 and 1 and 3 is carry now.)
• Now 15’square=225+earlier carry i.e.3=228
• So Final Answer is 22801
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CommentsLoading...
Great hub...will add this to my resource list for my students.
hey good hub i can use it with my kids also thanks
Learning to square a number is good, but it is good know how to do any 2 by 2 caluation. For example 51 x 51 (think 5 times 5 is 25, so add the 1 to make 26. 1 squared is 01. answer 2601) Great, how did I do that? 51 x 51 is not hard to see laid out in this way. Look at the left number and muliply. You will have 25. Next multiply and add the inside and outside pairs of number. The inside numbers are the 1 of 51 and the 5 of the other 51. They add up to 5 plus 5 or 10.
Place the 1 of 10 OVER 5 of 25. (25 + 10 = 260) All that is left if the right most numbers 1 times 1, which is 1. Place this at the end of the number. 2601
The masterkeys of this technique is that you add the tens unit of numbers and only attach the ones unit. Give it a try.
Wonderful blog!
It's gr8.
But how to square 24 or 34 or like that.
According to ur formula:
24'square=2 X (24+2)/6????
Would you please do it?
Hey man,
why did u delete the video??
thank u but plz i wanna more..................
2*(24+4)/4
2*28/4
56/16
56+1/6
Ans: 576
hey all these are usual
this realy helped but.......
need more methods!!!
Really helpful!
This was very helpful it rlly helps us practice math!
excellent technique. good job done by the blogger. i appriciate his/her work. accept my thnks.
nothing like this its a great stuff continue your good work and i forgot to say very very than Q
i was hoping to get rid of timing difficulty during exams.i think you helped doing so.thank you.....................,,,,,,,,,,,,,,,,,
Wonderful stuff
What about 3 digit numbers
Thanks.Its really Helpful
nice
IT is a good effort
confusing
THANKS FRIENDS !!
THANKSSSSSS
What abt the 3digit cubes
definitely,it will ease the calculation
given:a=b
:. a^2=ab
a^2-b^2=ab-b^2 (subtractin b^2 from both sides)
ie (a+b)(a-b)=b(a-b)
:. a+b=b........(cancelling a-b on both sides)
ie 2=1
but dis isn't possible
explanation please???
bhanger! bhanger! bhanger!
very confussing but good so thx
quite easy thanq
Intersting
these are fabulous
I really thanks for this I am greatly helpful by this
@ CLVRKID
Since a=b and a-b = 0, you cannot cancel 0 on both the sides. Since anything multiplied by ZERO is always a ZERO. Hence your logic is wrong.
Its awsome but I want the square of numbers that does not end with 5 and 1.
Thank You so much! That really helped :)
nice cheap en easy fomulas
dsdsds
Excellent work done.
Thumbs up!!
Please can u do another blog on finding square roots.
That would be really helpful.
Thanks in advance
IT IS NICE BUT PLEASE TRY TO APPROACH THE VIDEO
thanks
Not so good
this is a metallllllllllllllllllll siteeeeeeeeeeee
I hav a master formula to compute squares upto 2 digit number in 5 sec I am working on 3 digit number and I will surely get sucess in it.. I am searching on internet..whether my formula already exist or not..til now it doesn't exist...I can also help u guys to fin cubes in one line and in less then 40 secs
Wow great tricks I also know how to caculate numbers fast in your head example 770times 20 first add oo then times 2 times 77 then your answer 15400 dats your answer
very nice , it really help full to me , thnx
good
good
not understooooooooooodable to me
amaclane 3 years ago
Wow, that's great stuff. You could do this in your head with a little practice... Thanks!