Warp Math Squaring

Do you know, if you square “nine ones” after they have been chained together, you will get a nice palindrome? For your information, a palindrome is a number that remains the same when its digits are reversed. It looks somewhat like this! (111111111)^2 = 12345678987654321 This symmetrical number reads the same backward, as forward. Are you trying to verify this fact? Don’t you think it will consume a lot of time? And we know time is very precious. What do we do then? Don’t you worry! We have a bunch of best tricks to calculate square numbers, that will mould you to think like a mathematician. So, let’s begin!