PA-28 Flight Instructor reported the aircraft immediately yawed to the left upon touchdown and took the controls from the student but the aircraft went off the runway and into the dirt. As the reporter managed to get the aircraft back onto the runway; the front wheel dropped into a depression in the dirt and a propeller strike occurred.

Narrative

On Day 0 at approximately XA:20 hours; I was conducting flight instruction in Aircraft X at ZZZ. My student was in the left seat; at the controls of the aircraft. At the time; we were practicing a short-field landing. We were descending on short final to Runway XX. The reported winds at the time were 160 at 6 kt. and the windsock on the field was indicating the same direction; but a lower wind velocity. Our approach was stabilized; and we had full flaps extended. As we crossed over the threshold; I noted our airspeed was approximately 75 miles per hour; the recommended airspeed for a short-field landing in that aircraft. We rounded out; flared for a very short distance; and touched down. The plane immediately yawed to the left. I took controls and attempted to input rudder to the right to stay on the runway; but the plane continued to the left and exited the runway into the dirt area. I was able to get the plane under control and made a 180-degree turn to the left; away from the runway to ensure nobody was landing before I entered back onto the runway. As I rolled back to the runway; the front wheel dropped into a depression in the dirt; causing the propeller to strike the dirt. I continued onto the runway and parked adjacent to the FBO building.