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Shortcuts On Squaring Two-Digit Numbers Part One

Updated on October 9, 2009




A.      Squaring  2-digit  number  ending in one

Example One :    Square  51

Step One :    Take a two-digit  number ending in 1, then subtract 1 from it.

                        51 – 1  =   50

Step  Two :   Square the difference

                       50  *   50   =   2500

Step Three :   Double the difference in step one  1 and add it to the square in step two              

                                       2500 + 100  =  2600

               Step Four  :    Add   1 to the sum in step three

                                        2600 +  1  =  2601

                                      Therefore  51 * 51  =  2601


             Example two :  Square the number  71

             Step one :    71 –  1  =  70

             Step two  :   70   *   70   = 4900

             Step three :      4900 + 140   =   5040

             Step four :           5040 + 1 =  5041

                Therefore             71 * 71  =   5041


B.      Squaring a 2-digit number ending in 2

Example One :  Square  62

Step One : Take a two-digit number ending in 2. If the number is 62, the last digit in the square

 is 4 .      _  _ _ 4

Step two : Multiply the first digit by 4 =è    6 * 4   =   24

The second digit in the produc t will be the next to the last digit  in the square. Keep any carry.

                            _ _ 4 4

Step three:  Square the first digit and add the number carried from the previous step.

                           6 * 6   = 36

                           36 + 2 =  38

Threfore the square of 62  is  3844

Example two :   Square 72

First step   :  2 * 2  = 4

Second step :   7 * 4  =  28    =è                _ _ 84

Third  step  : 7 * 7  = 49   ==è    49 + 2   =   51

         Therefore   72 * 72  =   5184


C.      Squaring  a  2-digit number ending in 3.

Example one :  Square 53

Step one : Take a two-digit number ending in 3. The last digit of the square will be 9.

Step two : Multiply the first digit by 6. The second digit in the product will be the next number to

                  The last digit in the square . Keep any carry.

                   5  *  6  =   30

                      _ _  0 9

Step three : Square the first digit and add the number carried from the previous step .

                           5  *  5   =  25

                          25  +   3   =  28

            Therefore     53 * 53   =   2809


Example two :  Square  83

Step one :   3 * 3  = 9

Step two :  8 * 6  =  48

                    _  _ 8 9

Step three :  8 * 8 = 64

                        64 + 4 =   68

Therefore 83 * 83  =  6889


SOURCE :   MATH POWER by Divina Gracia T. Bandong.  








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    • empeen profile image


      9 years ago from India

      Good one, useful one, but I think in CASE I, two digit number ending with one, it is easier if we use

      (a + b)2 =a2 + b2 + 2.a.b


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