Our companions do not have effective methods of telling us "it hurts", or where it hurts. In fact, dogs are pack animals which instinctively hide their pain for survival purposes.
Radiographs help us get the full picture of dental health. Feline and canine teeth have roots that are much longer than ours, as you can see in the picture on the right below. The arrow indicates the gum line; the portion above the arrow is what we see with the naked eye, the other 2/3 can only be seen by radiograph.