Friday, January 28, 2011

Square: Some more examples

(101)^2 = (10^2) (2×10×1) (1^2) or (1^2) (2×1×01) {(01) ^2}
               = (100) (20) (1) or (1) (02) (01)
               = (100+2) (0) (1) or 10201
               = (102) (0) (1) or 10201
                = 10201 or 10201.
(102)^2 = (10^2) (2×10×2) (2^2) or (1^2) (2×1×02) {(02) ^2}
               = (100) (40) (4) or (1) (04) (04)
               = (100+4) (0) (4) or 10404
               = (104) (0) (4) or 10404
               = 10404 or 10404.
(105)^2 = (10^2) (2×10×5) (5^2) or (1^2) (2×1×05) {(05) ^2}
               = (100) (100) (25) or (1) (10) (25)
               = (100) (100+2) (5) or 11025
               = (100) (102) (5) or 11025
               = (100+10) (2) (5) or 11025
               = (110) (2) (5) or 11025
               = 11025 or 11025.
(124)^2 = (12^2) (2×12×4) (4^2) or (1^2) (2×1×24) (24^2)
               = (144) (96) (16) or (1) (48) (576)
               = (144) (96+1) (6) or (1) (48+5) (76)
               = (144) (97) (6) or (1) (53) (76)
               = (144+9) (7) (6) or 15376
               = (153) (7) (6) or 15376
                = 15376 or 15376.
(1835)^2 = (18^2) (2×18×35) (35^2)
                 = (324) (1260) (1225)
                 = (324) (1260+12) (25)
                 = (324) (1272) (25)
                 = (324+12) (72) (25)
                 = (336) (72) (25)
                 = 3367225.
(1836)^2 = (18^2) (2×18×36) (36^2)
                 = (324) (1296) (1296)
                 = (324) (1296+12) (96)
                 = (324) (1308) (96)
                 = (324+13) (08) (96)
                 = (337) (08) (96)
                 = 3370896.