What would happen if the dorsal root of a spinal nerve were completely transected?

There would be loss of sensory function

The dorsal root of spinal nerve is the part of the peripheral nervous system that picks up sensory signals / information and transmits the signal through the nerve to the brain. If the root is damaged or transected, the brain will no longer receive sensory messages from that nerve, which means that the patient will have loss of sensation in that area.