Squares

                                   Finding square of any number is very very easy and you can calculate it very fast But before
                                   going to concept  ,you should do some home work . You are well conversant  in squaring  of
                                   1 to 9
                                

                                        These are square from 1 to 9 . Now learn  square index of 1 to 9

                                                   Square  Index is nothing except table of 2 .We just double
                                                   number in first part ie from 1 to 4 and leave ten 's digit in
                                                   second part ie from 5 to 9  after doubling .
                                Steps                 Now learn main concept  by this example
                                                                    21 x21 =????
                                                  Here our last digit (or unit digit ) is1 .Its square index
                                                is 2  First we take square of 1 and write it extreme right then
                                                we take first digit and multiply it by the square  index write before
                                                 last figure  then  squaring first digit and write extreme left
                                                  If there is any carry add to it 
                                                                                                        
                                                    1x1 =1                 2x2 =4      2²  =4        4  4 1      Answer
                                                     

                                               44 X44=????
                                               Here square  index of 4 is 8 
                                               4x4 = 16             4x8 +1(carry ) =32 +1 = 33     4^{2   +  3}  =16+3  =19          1936     Answer

                                             93 X93 =????
                                             Here  square  index of 3 is 6
                                            
                                               3x3 =9          9x6 =54                9²+ 5 =81 +5 =86                    8649    Answer

                                            These are the square where last digit is 1 to 4  now we learn squaring of those numbers
                                            having last digit from 5 to 9.Method is same, instead of squaring first digit  multiply  to
                                             next digit            

                                               36 X36 = 

                                                Here square index  of 6 is 2
                                                
                                               6x6 =36          3x2 + 3 =6+3=9           6X(6+1) =   6 x7 =42                42 96  answer

                                          87 x 87 =

                                         Here  square index is 4

                                          7x7=49                 8x4+4 =32+4 =36           8x(8+1)+3 =72+3 =75                 75 69  Answer
 

                                         25x25 =

                                        Here square index is 0  so no need of middle step

                                        5x5 =   25                              2x(2+1) = 6                    625       answer
                          

                                           Now with the help of this concept we can calculate square of any number
                                            236 x 236=????

                                            Here square index of 6is 2 
                                              6x6 =  36    23 x2 +3 =46+3=49        23x24*+4 =552+4=556          55696       answer

                                             *23x24  = ?  By cross and vertical multiplication  method(covered in lesson no 7)
                                       4 / 14  /12     =        552    

                                                                                                  

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