SQUARING

Squaring is intimately connected with a procedure known as the Duplex Combination process.

Example: Duplex of 2 is 2²=4

If you want to know

Ex: 34²

Step I          :3² / 2(3x4) / 4²

Step II         :9 / 24 / 16 

Answer       :11/25/16 =>1156

Ex:346

Step I          : 3² / 2(3X4) / 2(3X6) + 4²/ 2(4X6) /6²

Step II         :  9 / 24             /          52      /48     /36

Answer       : 11 / 29 /                     57        /51      /36   =>119716

Ex:8432

Step I          : 8² / 2(8X4) / 2(3X8)+4² / 2(8X2) + 2(3X4) / 2(4X2) + 3²/ 2(3X2) /2²

Step II         :  64 / 64          / 64    /          56       /25     /12     /4

                    

Answer       :71 /70  /69      /58      /26      /12      /          4 => 71098624

Ex : 73214²=53464032682917916=>5360289796

Special cases like numbers end’s with 5 or begins with 5 there is easy steps

Square of number from 51 to 59

51²

Step I          5²+1 /1²

                     26 / 01=>2601

54²

Step I          5²+4 /4²

                   29/16=>2916

59²

Step I          5²+9 /9²

                   34/81=>3481

If 5 came end of the number

Ex: 15²

         1 x (1+1) / 5²

                2      /25=>225

Ex: 85²

           8 x (8+1) / 5²

                   72    /25=>7225

Ex: 115²

                11x (11+1) / 5²

                 132           /25=>13225