Curious facts about square numbers

Let me present some curious facts about square numbers-
1)Two square numbers when placed side by side will reveal another square number-Examples
Square numbers 1 and 225 will produce 1225 which is the square of 35.
Similarly 4 and  225 will produce 4225-square of 65
16 and 81 will produce 1681-square of 41
144(sq.of 12) and 2401(sq of 49) will produce 1442401(sq of 1201)
2)In the following cases the square numbers follow a pattern-
7*7=49...67*67=4489....667*667=444889.....6667*6667=44448889
4*4=16.. 34*34=1156....334*334=111556.....3334*3334=11115556
3)The sum of 20 and 25 is 45 while the square of 45 is 2025.
Similarly the sum of  30 and 25 is 55 while the square of 55 is 3025.
The sum of 494 and 209 is 703 while the square of 703 is 494209
The sum of 88 and 209 is 297 while the square of 297 is 88209.There are many more such cases
4)The square of 12 viz 144 and the square of 33 viz 1089 will add up to1233
5)The square of 13 is 169 ,while the square of 31 is 961
Similarly the square of 12 is 144,while the square of 21 is 441.
The square of 102 is 10404,while the square of 201 is 40401.
6) The square of 13 is 169 while 1,6 and 9 will add upto 16,As a surprise the square of 16 is 256 and the digits 2,5 and 6 will add up to 13.
7)The square of 45 is 2025.If you add 1 to each digit in 2025 you will have 3136 which is a square of 56
Similarly the square of 34 is 1156.If you add 3 to each digit in 1156 you will have 4489 which is a square of 67.
8)Though the dates are too far away even some dates will reveal square numbers if you remove the hyphens as shown below-
4-01-6016 ...the square of 2004 being 4016016
Similar cases date 1-01-6064....sq of 1008 being 1016064
Date  1-06-5024...square of 1032 being 1065024.There are also many more cases.