Wednesday, August 3, 2011

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

No comments:

Post a Comment