Square root of  11.1111111111....  is  3.333333333....
Square root of  1111.11111111....  is  33.33333333....

And the best part is, it seems to continue with all numbers containing an even amount of 1s before the decimal. For instance:

111111.1111111...
11111111.1111111...
1111111111.1111111...

Something I like about numbers, sometimes they're blatantly beautiful, all of the other times the beauty is cleverly hidden...

111,111,111 * 111,111,111 == 12,345,678,987,654,321

The concatenation of the prime number 11 with itself.

1111 equals 112 + 122 + 132 + 142 + 152 + 162. [De Geest]

1111 = 11 x 101 in base 10 and in base 2, where 11 and 101 are both prime in base 10 and base 2. [Shafer]

The sum of the digits of the first 100 primes. [Wilson]