Squaring 3 digit numbers ending in 1

There is a short cut method for squaring 3 digit numbers ending in 1 rather than going for normal multiplication. If you can practice a bit with this method then you can square such numbers in mind itself. Let me explain the method with an example.

Example : 341 ²

Step 1 : square the last digit 1 and put it in the last places of the result

 

       *****1

Step 2 : The second last digit can be found by doubling the tenth place digit of the number,

           here 4 ( 4 X 2 = 8).

      

       ****81

Step 3 : Square the tens digit and add the double of 100th digit to it
         4 ² + ( 2 X 3 ) = 16 + 6 = 22
         put 2 in the result and carry 2 forward.
        
         ****281

step 4 : multiply the first two digits of the number to be squared and double it i.e

      
      3 x 4  = 12 ; 12 x 2 = 24
       

       Now add the  carry forward  2      

        24  + 2 = 26

      

       Put 6 in the result and carry forward 2

    

       **6281

         

Step 4 : Square the 100^th position digit and add carry forward and put it to the result

 here 3 ² = 9; 9 + 2 = 11

        116281

 341 ² = 116281   

Example : 761 ²

Step 1 : square the last digit 1 and put it in the last places of the result

 

       *****1

Step 2 : The second last digit can be found by doubling the tenth place digit of the number,

           here 6 ( 6 X 2 = 12). Put 2 in the result and carry the 1 forward

      

       ****21

Step 3 : Square the tens digit and add the double of 100th digit to it

         6 ² + ( 2 X 7 ) = 36 + 14 = 50

        add the carry forward

         50 + 1 = 51

         put 1 in the result and carry 5 forward.

        

         ****121

step 4 : multiply the first two digits of the number to be squared and double it i.e

      

      7 x 6  = 42 ; 42 x 2 = 84

       

       Now add the  carry forward  5      

        84  + 5 = 89      

       Put 9 in the result and carry forward 8    

       **9121

         

Step 4 : Square the 100^th position digit and add carry forward and put it to the result

 here 7 ² = 49; 49 + 8 = 57

        579121

 761 ² = 579121