The Wiki has the goods on the big day…
Square root day is a humorous holiday celebrated on dates where the day and the month are both the square root of the last two digits in the current year. For example, the last square root day was March 3, 2009 (3/3/09), and the next square root day will be April 4, 2016 (4/4/16). The final square root day of the century will occur on September 9, 2081. Each century it is the same nine dates that are Square root days.
Ron Gordon, a Redwood City, California high school teacher, first created the day for 9/9/81. Gordon is the official public relations person and sends news releases to world media outlets. In addition, his daughter has got in on the act and set up a Facebook page for people to share how they were celebrating the day.