Vedic mathematics : Easy way of finding square of a number ending with 5

quick way to square numbers that end in 5 using the formula BY ONE MORE THAN THE ONE BEFORE.

• 75² = 5625 75² means 75 x 75.
  The answer is in two parts: 56 and 25.
  The last part is always 25.
  The first part is the first number, 7, multiplied by the number "one more", which is 8:
  so 7 x 8 = 56
• Similarly 85² = (8 * 9) 25 = 7225
  

Square of 2 digit number having same digit, AA

N     N^2
11   121
22   484
33   1089
44   1936
55   2916
66   4356
77   5776
88   7744
99   9801


Now suppose that number is AA
than AA = 10A+A
We know,
(a+b)^2 = a^2 + 2ab + b^2
AA ^ 2 = (10A +A) ^2 = 100*(A^2 ) + (A^2 ) + 2*10A*A= 121*(A^2 )
So all these numbers are divided by 121 :P

So if you want to find 99^2, you can do 121 * (9^2), though it may look tough this way.
=121 * 81
But for 22 ^2 = 121 * 4 = 484 , i.e. little easier

Squares upto 100

Number	Square
1	1
2	4
3	9
4	16
5	25
6	36
7	49
8	64
9	81
10	100
11	121
12	144
13	169
14	196
15	225
16	256
17	289
18	324
19	361
20	400
21	441
22	484
23	529
24	576
25	625
26	676
27	729
28	784
29	841
30	900
31	961
32	1024
33	1089
34	1156
35	1225
36	1296
37	1369
38	1444
39	1521
40	1600
41	1681
42	1764
43	1849
44	1936
45	2025
46	2116
47	2209
48	2304
49	2401
50	2500
51	2601
52	2704
53	2809
54	2916
55	3025
56	3136
57	3249
58	3364
59	3481
60	3600
61	3721
62	3844
63	3969
64	4096
65	4225
66	4356
67	4489
68	4624
69	4761
70	4900
71	5041
72	5184
73	5329
74	5476
75	5625
76	5776
77	5929
78	6084
79	6241
80	6400
81	6561
82	6724
83	6889
84	7056
85	7225
86	7396
87	7569
88	7744
89	7921
90	8100
91	8281
92	8464
93	8649
94	8836
95	9025
96	9216
97	9409
98	9604
99	9801
100	10000