Shortcut Squaring Techniques

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Friends, we have already discussed two shortcut methods for finding squares of a given number. You can find the Shortcut method 1 from here and Shortcut method 2 from here. Today we are giving you another simple method to find the squares of numbers ending with 9 and 1. This method is shared by our friend Mr. Hareesh Kumar. As you know, both the numbers 9 and 1 have a sort of similarity and make us easy to find the squares of such numbers within fraction of seconds. Let us have a look at them, lets start with numbers ending with “9”:

NUMBERS ENDING WITH 9:

Let me start from smaller numbers.

Ex. 1: 9^2 = ?    (Of course everyone know very well about this)

Sol: We know that, 10^2 = 100

       Step – 1: Consider the 10’s digit of “10”, which is 1.

       Step – 2: Double the number in the ten’s digit (i.e., 1*2 = 2)

               (We know that, the unit’s digit of the square of a number ending with 9 will be 1)

       Step – 3:  Subtract the doubled number from the number formed by eliminating a zero (0)

                     from the resultant of the 10^2. (i.e., 10 – 2 = 8)

      Step – 4: This is the final step, place 8 before 1, hence the answer becomes “81”

Ex. 2: 29^2 = ?

Sol: 30^2 = 900; 3*2 = 6 --> 90 – 6 = 84

                Therefore, 29^2 = 841

Ex. 3: 139^2 =?

Sol: 140^2 = 19600 ; 14*2 = 28 --> 1960 – 28 = 1932

                Therefore, 139^2 = 19321

Ex. 4: 89^2 =?

Sol: 90^2 = 8100; 9*2 = 18 --> 810 – 18 = 792

                Therefore, 89 * 89 = 7921

Ex. 5: 249^2 =?

Sol: 250^2 = 62500; 25*2 = 50 --> 6250 – 50 = 6200

               Therefore, 249^2 = 62001

NUMBERS ENDING WITH 1:

Ex. 6: 11^2 =?

Sol: We know that, 10^2 = 100

           Step 1: Double the tens’ digit of 10. (i.e., 1*2 = 2)

            Step 2: By eliminating zero in the unit’s place in the resultant of 10^2, we get 10. 

                         Add 2 to this 10 --> 12

            Step 3: We know that the result obtained by squaring a number ending with 1 will also contain 1 in its unit’s digit.

            Step 4: Place the 12 before 1 --> Answer = 121

Ex. 7: 121^2 =?

Sol: 120^2 = 14400; 12*2 = 24 --> 1440+24 = 1464

                Therefore, 121^2 = 14641

Ex. 8: 91^2 =?

Sol: 90^2 = 8100; 9*2 = 18 --> 810+18 = 828

                      Hence, 91^2 = 8281

Ex.9: 231^2 =?

Sol: 230^2 = 52900; 23*2 = 46 --> 5290+46 = 5336

                        Hence, 231^2 = 53361

Ex. 10: 501^2 =?

Sol: 500^2 = 250000; 50*2 = 100 --> 25000+100 = 25100

                        Hence, 501^2 = 251001

Thanks to Hareesh Kumar for the update :)

Already know this method ? You can find more shortcuts from here

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