Squaring of number without calculator in seconds

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hello guys this is the one of the most common question i was asked is.----

is there any way that i can square any number in less then 5 seconds sir.

And the answer is surely yes


so, let the blog begin

we will learn here squaring the numbers starting from 1-110
I think learning this would be enough in any course of action
later we will learn squaring the remaining numbers from 111 onwards

we will divide this topic into four sections as written below
  1. squaring numbers from 1-10 
  2. squaring numbers from 11-20
  3. squaring numbers from 40-60
  4. squaring numbers from 90-110
  5. squaring numbers accept all these 

  1.  Squaring numbers from 1-10 

    i think we don't need any type of trick to learn the squares of these 10 starting numbers 
    these are too easy to memorize. This will also help in squaring the number of other tricks
    so, if you have not learnt the squares of these number please go through it

                numbers                                         Squares

    • 1                                =                      1
    • 2                                =                      04
    • 3                                =                      09
    • 4                                =                      16
    • 5                                =                      25
    • 6                                =                      36
    • 7                                =                      49
    • 8                                =                      64
    • 9                                =                      81
    • 10                              =                      100
     

  2. Squaring number from 11-20 

    now we will square the numbers from 11-20
    i will make you understand with the help of an example
     let's take an example of 13

     step 1. adding the once placed number to the selected number   
                i.e.: 13 + 3 ( 13 - underlined number is once placed number )
                       = 16

    step 2.  multiplying the above number to 10
                 i.e.: 16*10
                        =160
    step 3. Now square the once placed number and add it to the above number
                i.e.: A. 3*3 = 9 and 160 + 9 = 169

    And we have got the answer 169

    trust me guys this is the mind process of just 2-3 seconds
    so take a number and try this trick
      

    3.  Squaring numbers from 40-60

            this is simplest trick ever to square the numbers from 40-60
              You can square the numbers 40 as 1600 and 60 as 3600
             using your memorized number squares of 4 and 6
             but what about other numbers so use this trick
              let us take an example of 46 and 54

          Step 1. classify the numbers into less than 50 ( <50 ) and above than 50 ( >50 )

          Step 2. Now calculate how much the number is less than or more than 50
                 i.e.: 50 - 46 = 4 ( means 46 is 4 less than 50)
                  and 54 - 50 = 4( means 4 more than 50)

           Step 3. Now if your number is less than 50 than minus the number you obtained above
                    (  after 50-46=4) i.e.: 25 - 4 = 21
              
                  and if your number is more than 50 than add the number obtained above to 25
                   ( after 54 -50 = 4) i.e.: 25 + 4 = 29
                  Now this you first two digit i.e.: 21_ _    and 29_ _

     Step 4. now square the number you obtained in step 1
                 i.e.: 4 ( when 46 )    and 4*4 = 16
                        4 ( when 54)     and 4*4 = 16
    ( in case you get the squares like 1 ( 1*1 = 1 ), 4 ( 2*2 = 4) and 9 ( 3*3 = 9)
      then use 0 in the  tens place i.e.: 01,04,09

    Step 5. place the number you obtained above to the 3rd and 4th place
                 i.e.: 2116
                 i.e.: 2916
    and this is you final answer

     

  3.  Squaring number from 90 - 110

    let us take an example of 92 and 106

     Step 1. find out the difference between 100 and your number
                  i.e.: when 92 then 100 - 92 = 08
                  i.e.: when 106 then 106 - 100 = 06

    Step 2. Square the number you obtained above              
     
                i.e.: 8*8 = 64
                i.e.: 6*6 = 36
          Step 3. Now minus the number obtained in step 1 from your number if your number is less than 100 and add the number if your number is greater than 100

                       i.e.: 92 - 8 = 84
                      i.e.: 106 + 6 = 112
          Step 4. Place the above number in the 1st place and squared number in the 2nd place 
                       i.e.: 8464
                       i.e.: 11236

and this is your final answer




          5. squaring the remaining number

                now remaining numbers can be squared using this algebric formula                    
                ( a+ b )2  = a2 +b2 +2ab
                 for example you will divide 74 into 70+4
                 and then solve as 
                    ( 70 + 4 )2  = 702 +42 +2*70*4
                    = 4900+16+560 = 5476

 this will take a little time to calculate but still you can calculate it faster than the calculator
so, thank you for visiting here 
you will find here all these types of facts and amazing tricks like this

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