As there are 81 tiles total, that makes your area 81. Being a square, that makes your area equation A=s^2. As you need a side, this makes your equation s=√A. Plugging in 81 as A, we get s=√81=9, so an edge has 9 tiles.
The answer oils be 2 square root 2 because 4 times 2 is 8 and because the square root of 4 is 2 you would move that 2 to the outside and keep the other two on the inside of the square root.