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How to square numbers easy and fast using Vedic Mathematics?

Updated on August 4, 2012
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

Comments

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    • profile image

      Sanskriti 15 months ago

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

    • profile image

      Arun Pratap 2 years 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

    • Ankit Vyas profile image

      Ankit kumar 2 years ago from khatauli

      root 135 ki value short cut r cube

    • Ankit Vyas profile image

      Ankit kumar 2 years ago from khatauli

      multiply 4 digit 3 digit answer on line

    • Ankit Vyas profile image

      Ankit kumar 2 years 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 kumar 2 years 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 kumar 2 years 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 kumar 2 years 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

    • profile image

      ankit kumar 2 years ago

      2 root 5927 value

      r 3root four digit value answer

      r 4digit×3digit

      to answer 1 line please easy to

      use any examples

    • profile image

      ankit kumar 2 years ago

      2 root 5927 value

      r 3root four digit value answer

      r 4digit×3digit

      to answer 1 line please easy to

      use any emple

    • profile image

      Rahul Kumar 2 years ago

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

    • profile image

      anjali 2 years ago

      nice i like it hub

    • profile image

      santu 2 years 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!!

    • profile image

      ujwala 2 years ago

      Its very interesting, or amazing methods,

      Plz upload some mathematical models for teaching material

    • profile image

      sachin kumar lamba 3 years ago

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

    • profile image

      sachin kumar lamba 3 years ago

      Kya koi mujko 4 digit ka squire batayega jaise 1552 ka

    • profile image

      pankaj 3 years ago

      it is vry helpful for me

    • profile image

      anurag 3 years ago

      Its vry helpful for me.... Thnxxx

    • profile image

      sandeep 3 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

    • profile image

      Apurva 3 years ago

      Very helpful to us! Thanx..

    • profile image

      shiva 3 years ago

      Its really killer . I must say wow¶ ..

    • profile image

      Rohan Sharma 4 years ago

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

      as (a-b)=0 in your case

    • profile image

      Nidhi 4 years ago

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

    • profile image

      honey singh 4 years ago

      i want 4digit no. square

    • profile image

      himanshu 4 years ago

      i love methods but most easier then it i also want

    • profile image

      Anisha 4 years ago

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

    • profile image

      KRISPY 4 years ago

      I WANT THE SQUARE ROOT BY THIS FORMULA:

      A2/2AB/B2

    • profile image

      dustin340 4 years ago

      i know an easy method for squaring numbers 50-59

    • profile image

      amar 4 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

    • profile image

      spoubselo 5 years ago

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    • profile image

      PRASAD PANDURANG KURLEKAR 5 years ago

      excellent post....thank you

    • profile image

      Akansha 5 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

    • profile image

      Nilesh Tiwary 5 years ago

      Thanks a lot.....

    • profile image

      mad 5 years ago

      very helpfulllllllllllll

    • jpcmc profile image

      JP Carlos 5 years ago from Quezon CIty, Phlippines

      This is really interesting.

    • profile image

      shanu 5 years ago

      i could not understand these tricks

    • profile image

      emily 5 years ago

      really good im much better at maths

    • profile image

      ajay 5 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.

    • profile image

      girl 5 years ago

      its interesting, bt i hav a very gud formula 2

    • profile image

      jigar gandhi 5 years ago

      very nice , it really help full to me , thnx

    • profile image

      clayrapheal 5 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

    • profile image

      shwetank pandey 5 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

    • profile image

      N SRI HARSHA 5 years ago

      IT IS NICE BUT PLEASE TRY TO APPROACH THE VIDEO

    • profile image

      Ronaldo Ka baap 5 years ago

      Please can u do another blog on finding square roots.

      That would be really helpful.

      Thanks in advance

    • profile image

      Yash 5 years ago

      Excellent work done.

      Thumbs up!!

    • profile image

      Manasi 5 years ago

      Thank You so much! That really helped :)

    • profile image

      Venky 5 years ago

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

    • profile image

      Mahavir 5 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.

    • profile image

      harsh 5 years ago

      I really thanks for this I am greatly helpful by this

    • profile image

      utkarsh tarika 5 years ago

      these are fabulous

    • profile image

      jake 5 years ago

      very confussing but good so thx

    • profile image

      CLVRKID 6 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???

    • profile image

      mohd atif 6 years ago

      definitely,it will ease the calculation

    • profile image

      Sonia 6 years ago

      What abt the 3digit cubes

    • profile image

      Arun 6 years ago

      IT is a good effort

    • profile image

      aayushi 6 years ago

      nice

    • profile image

      Guest 6 years ago

      Thanks.Its really Helpful

    • profile image

      Hugh 6 years ago

      What about 3 digit numbers

    • profile image

      Madhu 6 years ago

      Wonderful stuff

    • profile image

      akshay 6 years ago

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

    • profile image

      philosanil 6 years ago

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

    • profile image

      yatish mittal 6 years ago

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

    • profile image

      thnx 6 years ago

      This was very helpful it rlly helps us practice math!

    • profile image

      Guest1 6 years ago

      Really helpful!

    • profile image

      varshi 6 years ago

      this realy helped but.......

      need more methods!!!

    • profile image

      jake 7 years ago

      hey all these are usual

    • profile image

      prafulla 7 years ago

      2*(24+4)/4

      2*28/4

      56/16

      56+1/6

      Ans: 576

    • profile image

      tanaya 7 years ago

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

    • profile image

      Mohit 7 years ago

      Hey man,

      why did u delete the video??

    • profile image

      Mohit 7 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?

    • profile image

      Robin 7 years ago

      Wonderful blog!

    • profile image

      John 8 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.

    • profile image

      jyoti 8 years ago

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

    • profile image

      Maths tutor 8 years ago

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

    • profile image

      amaclane 8 years ago

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