How to square numbers easy and fast using Vedic Mathematics?

Squaring Numbers in seconds
Squaring Numbers in seconds

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 an 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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Comments 75 comments

amaclane 7 years ago

Wow, that's great stuff. You could do this in your head with a little practice... Thanks!


Maths tutor 7 years ago

Great hub...will add this to my resource list for my students.


jyoti 7 years ago

hey good hub i can use it with my kids also thanks


John 7 years ago

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.


Robin 6 years ago

Wonderful blog!


Mohit 6 years ago

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?


Mohit 6 years ago

Hey man,

why did u delete the video??


tanaya 6 years ago

thank u but plz i wanna more..................


prafulla 6 years ago

2*(24+4)/4

2*28/4

56/16

56+1/6

Ans: 576


jake 6 years ago

hey all these are usual


varshi 5 years ago

this realy helped but.......

need more methods!!!


Guest1 5 years ago

Really helpful!


thnx 5 years ago

This was very helpful it rlly helps us practice math!


yatish mittal 5 years ago

excellent technique. good job done by the blogger. i appriciate his/her work. accept my thnks.


philosanil 5 years ago

nothing like this its a great stuff continue your good work and i forgot to say very very than Q


akshay 5 years ago

i was hoping to get rid of timing difficulty during exams.i think you helped doing so.thank you.....................,,,,,,,,,,,,,,,,,


Madhu 5 years ago

Wonderful stuff


Hugh 5 years ago

What about 3 digit numbers


Guest 5 years ago

Thanks.Its really Helpful


aayushi 5 years ago

nice


Arun 5 years ago

IT is a good effort


Sonia 5 years ago

What abt the 3digit cubes


mohd atif 5 years ago

definitely,it will ease the calculation


CLVRKID 4 years ago

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???


jake 4 years ago

very confussing but good so thx


utkarsh tarika 4 years ago

these are fabulous


harsh 4 years ago

I really thanks for this I am greatly helpful by this


Mahavir 4 years ago

@ 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.


Venky 4 years ago

Its awsome but I want the square of numbers that does not end with 5 and 1.


Manasi 4 years ago

Thank You so much! That really helped :)


Yash 4 years ago

Excellent work done.

Thumbs up!!


Ronaldo Ka baap 4 years ago

Please can u do another blog on finding square roots.

That would be really helpful.

Thanks in advance


N SRI HARSHA 4 years ago

IT IS NICE BUT PLEASE TRY TO APPROACH THE VIDEO


shwetank pandey 4 years ago

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 success 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


clayrapheal 4 years ago

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


jigar gandhi 4 years ago

very nice , it really help full to me , thnx


girl 4 years ago

its interesting, bt i hav a very gud formula 2


ajay 4 years ago

CLVRKID , here is your answer in your 4 to 5th step you are dividing a+b*a-b/a-b = b, this step is wrong as a-b = 0(a=b) so it becomes a+b*0/0 0/0 is not equal to one it is any no.(as 0*any thing is 0). and to this blog great and an info.this vedic maths developed over a period of 5000-3000 bc.longggggg before the world. romans invented the roman numeral system (I,V,X,...) which is very complicated and even multiplication becomes a monumental task then algebra,trinometry,calculus all are impossible but indians invented the numeral system(1,2,3,4,5,6,7,8,9,0) 2500 years before romans. great right. for them no need of calculator their mind is the calculator.with this advanced maths they invented calculus,0,numeral system,place value system e.t.c and they also flourished in astronomy,science and medicine hattts off to ancient indians.


emily 4 years ago

really good im much better at maths


shanu 4 years ago

i could not understand these tricks


jpcmc profile image

jpcmc 4 years ago from Quezon CIty, Phlippines

This is really interesting.


mad 4 years ago

very helpfulllllllllllll


Nilesh Tiwary 4 years ago

Thanks a lot.....


Akansha 4 years ago

Similar to the cubes formula

if you have a two digit no: that u want to square then let a=tens digit

b=units digit

a square+ 2ab+b square

for example: (13)2

a square= 1

2ab=6 (2+3*1)

b square = 9


PRASAD PANDURANG KURLEKAR 4 years ago

excellent post....thank you


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amar 3 years ago

how to do square for a three digit number when u square the last digit and get two digit number for unit place...like 146^2


dustin340 3 years ago

i know an easy method for squaring numbers 50-59


KRISPY 3 years ago

I WANT THE SQUARE ROOT BY THIS FORMULA:

A2/2AB/B2


Anisha 3 years ago

Can you tell me how to square in case of 4 digit number


himanshu 3 years ago

i love methods but most easier then it i also want


honey singh 3 years ago

i want 4digit no. square


Nidhi 3 years ago

Very easy.......thanks forthe resourse


Rohan Sharma 2 years ago

CLVRKID, that's because no one can cancel a zero from a zero...

as (a-b)=0 in your case


shiva 2 years ago

Its really killer . I must say wow¶ ..


Apurva 2 years ago

Very helpful to us! Thanx..


sandeep 2 years ago

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.

/!’square !=1 do correct it i have no problems but just to be 100% perfect


anurag 2 years ago

Its vry helpful for me.... Thnxxx


pankaj 2 years ago

it is vry helpful for me


sachin kumar lamba 24 months ago

Kya koi mujko 4 digit ka squire batayega jaise 1552 ka


sachin kumar lamba 24 months ago

Kya koi mujko 4 digit ka squire batayega jaise 1552 ka short method


ujwala 22 months ago

Its very interesting, or amazing methods,

Plz upload some mathematical models for teaching material


santu 21 months ago

it's so nice - This is a very simple and works exactly Vedic Mathematics terribly early .A simple method of identifying who gave me and I love him vedic maths.Plz upload some mathematical models for teaching material!!


anjali 17 months ago

nice i like it hub


Rahul Kumar 16 months ago

Okay now how to calculate the square of 228 mentally.., Please reply the answer.


ankit kumar 15 months ago

2 root 5927 value

r 3root four digit value answer

r 4digit×3digit

to answer 1 line please easy to

use any emple


ankit kumar 15 months ago

2 root 5927 value

r 3root four digit value answer

r 4digit×3digit

to answer 1 line please easy to

use any examples


Ankit Vyas profile image

Ankit Vyas 15 months ago from khatauli

2 root 5927 value

r 3root four digit value answer

r 4digit×3digit

to answer 1 line please easy to

use any examples


Ankit Vyas profile image

Ankit Vyas 15 months ago from khatauli

55 square=5×(55+5)/25=305/24=3075

but 23 cube kya hoga

55 cabe kya r kasa hoga reply fast


Ankit Vyas profile image

Ankit Vyas 15 months ago from khatauli

55 squre 5×(55+5)/25=300/25=3025

par 55 cube kya hoga

root 5929 ki value

and cube 3root 4913 value kya hogi in short form


Ankit Vyas profile image

Ankit Vyas 15 months ago from khatauli

2 root 216 ki value in short not long aagr root (12) a2/2ab/b2=value ha to (13) cube ki value kya hogi


Ankit Vyas profile image

Ankit Vyas 15 months ago from khatauli

multiply 4 digit 3 digit answer on line


Ankit Vyas profile image

Ankit Vyas 15 months ago from khatauli

root 135 ki value short cut r cube


Arun Pratap 13 months ago

Hey I am to intreseted to discover the squareing techniques..

I have discoverd a formula for squaring a number ending with 1...

(num *num ++ 2*num ++ 1 remains constant). ...

11*11= 1*1++2*1++1== 121

51*51=5*5++2*5++1== 2601


Sanskriti 2 months ago

Its astonishing so difficult topic was made easy by just a few formulae

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