March 3, 2009 or 3/3/09 was called a "square root day" because the day and the month are both the square root of the last two digits of the year. The number of square root days between January 1, 2012 and December 31, 2099 is
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
First recognize that the day and the month must be equal.

Next, since $3^{2}=9$ and $10^{2}=100$, both the day and the month must be larger than 3 but less than 10 so that the year lies between 2012 and 2099.

We list all possible square root days in the table below.

| Day and Month | Last Two Digits of the Year | Date |
| :---: | :---: | :---: |
| 4 | $4^{2}=16$ | $4 / 4 / 2016$ |
| 5 | $5^{2}=25$ | $5 / 5 / 2025$ |
| 6 | $6^{2}=36$ | $6 / 6 / 2036$ |
| 7 | $7^{2}=49$ | $7 / 7 / 2049$ |
| 8 | $8^{2}=64$ | $8 / 8 / 2064$ |
| 9 | $9^{2}=81$ | $9 / 9 / 2081$ |

Since these are all actual dates between January 1, 2012 and December 31, 2099, then the number of square root days is 6 .