Squaring Technique to speed up calculations

Many readers have requested me to teach them a simple method to square two and three digit numbers. In bank exams calculation speed is very crucial. So today I have decided to explain my Squaring technique.

Technique

In case of two digit number deduct last digit and add it to another number and then add square of same.

In this technique we simplify the squaring method by making one unit's digit zero. It is far easy to multiply 50*24 than 54*24. So I used this technique. Try practice more to become expert in this technique.

Let's take some examples 


Find square of 53.
=(53*53)
= (53+3) * (53-3) + (3*3)
=(56*50) + 9
= (560*5) + 9
= 2800 + 9 = 2809   

Let's take another example 
Find square of 69
= (69*69)
= (69+1) * (69-1) + (1*1)
= (70*68) + 1
= (680*7) + 1
= 4761

Let's take one more example
Find square of 45
= (45*45)
= (45-5)*(45+5) + (5*5)
= (40*50) + 25
= 2000+25
= 2025

Comment below in case you find any problem in this technique.
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46 comments:

  1. hello sir....in 53 square u have taken 3*3 and in 69 square u have taken 1*1....can u tell me y u have taken and the trick?

    ReplyDelete
    Replies
    1. =69*69
      =(69-9)*(69+9)+(9*9)
      =60*78+81
      =(780*6)+81
      =4680+81
      =4761

      Delete
    2. (a^2 - b^2) = (a+b)(a-b)

      a^2= (a+b)(a-b) + b^2

      Delete
  2. thanku sir.... :) ur website is very helpful .

    ReplyDelete
  3. Yes use same technique

    ReplyDelete
  4. sir how to square more then 2 digits no?same techcnique will be implemented or not?

    ReplyDelete
  5. very good technique thanks sir

    ReplyDelete
  6. Hello Sir, You are doing very good :)

    ReplyDelete
  7. how to multiply with which no. how it will come to know

    ReplyDelete
  8. Wow, its really fantastic technique. .By using like this techniques we can surely increase our mathematical speed in any competitive exms. .thank you

    ReplyDelete
  9. why u r using 1 instead of 9 while squaring 69

    ReplyDelete
    Replies
    1. you can use 9 also but its easy to use 1. Main idea is to come to tens digit by whatever addition or subtraction.

      Delete
  10. Sir is it necessary to mug up the sqiare roots till 30.

    ReplyDelete
  11. I know other technique bt from 26 to 75 squares for that 1 should know squares of 1 to 25, which i feel is better than this technique bcoz u dont need to multiply any but v should do addition. I'm taking the same examples given here

    53 square = 2500+(100*number more than 50)+square of the increased number
    i.e

    IF THE NUMBER IS MORE THAN 50 DO SQUARES AS BELOW
    Square of 53 = 2500 + 300 + 9 = 2809
    Square of 69 = 2500 + 1900 + 361 = 4761

    NOW IF THE NUMBER IS BELOW 50, DO AS BELOW
    Square of 45 = 2500 - 500 + 25 = 2025

    ReplyDelete
    Replies
    1. Thanks for your contribution.
      Your trick is really good. But while finding square of 83, I found it really long.

      Delete
  12. Square between 75-100
    1.assume ,we have to find the square of N.first find the differencecwith 100 (lets say the difference isD)
    2.find the square of D it will give us the last two digits if square
    3.find N-D. It will give us the first two digits of the square
    example:
    Square of 93
    100-93=7
    7*7=49
    93-7=86
    So 8649
    Collected from bank power app

    ReplyDelete
  13. its very nice trick i liked it

    ReplyDelete
  14. sir your shortcut tricks were quite good but i would like to know about short cuts for imperfect squares and cubes

    ReplyDelete
  15. jst i want 2 know how to find cubes in simple process

    ReplyDelete
  16. Good techniques sir.keep it up..what is for 3 digits number??

    ReplyDelete
  17. CASE I

    squaring any 2 digit no..
    Eg. 83
    split 83 to (8|3)^2
    8^2=64 and 3^2 =9
    8*3*2 =48

    64|09
    +4|8
    ____
    6889


    CASE II

    Squaring any 3 digit no..
    Split it into 2 parts
    Eg.128
    (12|8)^2

    12^2=144
    8^2=64
    12*8*2=192

    144|64
    +19|2
    _____
    16384


    CASE III

    Squaring any number ending with 5
    Eg. 85
    Last 2 digit is 25
    Remaining digit is 8*(8+1)
    i.e) 8*9 =72

    85^2= 7225


    ReplyDelete
  18. Nice trick. great.....

    ReplyDelete
  19. Nice trick... Great. It make square calculation so easy.

    ReplyDelete
  20. I m giving one more trick may b some people will understand this method...
    from number 35 to 75
    1. Take value 25 for all squares between this range
    2. Square of 48.
    3. Take a mid 50 for all.
    4. Calculate how less the value is less than 50 then minus it from 25. And the result is 23 and calculate the square of less value i.e. Square of 2 because value is 2 less from fifty the result is 04
    5 merge these values result is 2304.

    ReplyDelete
  21. my trick take 53
    first take its square 2509 then 5*3=15*2=30 add it like this
    2509
    30
    2809 simpleeeeeeeeeeeeeeeeeeeeeee

    ReplyDelete
    Replies
    1. yes nice trick... I'm also posting the same trick here...
      For 2 digit no, adding unitdigit with 10's
      For 3 digit no, adding unitdigit with 100's
      EG:1004 Split it into two parts : If second part has 2 digits then
      10|06
      100|0066
      1|20
      +_______
      1012036

      Delete
  22. Squaring Technique for numbers having same digits...

    >>111 Here there are 3 ones,
    so write 123 and in reverse also 321. bt the middle term is common
    12321

    >>1111 Here 4 ones. 1234321

    >>33 here 2 three's are there
    3^2=9
    write it as _0_9 (single digit gap b4 each digit)
    Fill the first gap with next number of 0 i.e)1
    Fill the second gap with previous number of 9 i.e) 8
    ANS : 1089

    >>333
    write it as _ _ 0 _ _ 9
    Ans : 1100889

    Same technique can be applied for 6 and 9

    >>666 (6^2 = 36)
    write it as _ _ 3 _ _ 6
    Ans : 443556

    >>999 (9^2 = 81)
    write it as _ _ 8 _ _ 1
    Ans : 998001


    ReplyDelete
  23. Thanks I got easy technique

    ReplyDelete
  24. sir how can we do squaring of 4 digits like...1432 nd more than 4 digits like...5432819 etc with shortcuts ?

    ReplyDelete
  25. hello sir how can we find out the sqaure of 1432 with shortcuts nd more than 4 digits like 73214,5432819 etc ?

    ReplyDelete
  26. 45*45 this another simple way is take last digit multiply 5*5=25....................then take 4 next number of 4 is 5 so multiply both we get 4*5 =20 so 45*45= 2025

    ReplyDelete
  27. please tell the method of squaring 149*149

    ReplyDelete
    Replies
    1. (150-1)*(150-1)=22500+1-2(150)=22201

      Delete
  28. 149*149 => FIRST ADD 149 WITH 49 OF SECOND DIGIT 149+49=198 THIS IS OUR FIRST PART ANSWER FOR SECOND PART JUST MULTIPLY 49 OF FIRST ONE WITH 49 OF SECOND ONE =49*49 NOW WE HAVE ALREADY GET FIRST PART NOW SECOND PART JUST ADD BOTH OF THEN AS

    198
    2401
    22201

    ReplyDelete
  29. hello sir....in 53 square u have taken 3*3 and in 69 square u have taken 1*1....can u tell me y u have taken and the trick?

    ReplyDelete
  30. Replies
    1. by using this formula ,u can find out square of any number.
      square of 45=?
      a=4,b=5
      use it a^2+2ab+b^2 ,put last digit only and remaining will be remainder.
      2025

      Delete
  31. BERBIYA YOUR TECHNIQUE IS SO NICE THANKS FOR GIVING YOUR IDEA.

    ReplyDelete
  32. HI BARBIA YOUR TECHNIQUE IS REALLY NICE BUT I HAVE A DOUBT IN THAT CAN YOU PLEASE CLARIFY THAT.IN FINDING CUBE ROOTS I HAVE NO DOUBTS IN FINDING 666 AND 333 AND 999 IS SO BUT THE SAME FORMULA IS NOT APPLICABLE FOR FINDING 444 AND 555 Y I AM CONFUSED PLEASE CALRIFY MY DOUBT SIR

    ReplyDelete

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