Can Toothbrushes Remove Tartar?

Simply put, no. But let’s talk a little about what tartar and plaque is first. Plaque is a collection of bacteria and their waste products that builds up on teeth (and other surfaces in the mouth). Plaque is sticky and colourless when it first forms, and is easily removed by proper oral hygiene procedures (i.e. toothbrushing and flossing).
Plaque that is left on the teeth can irritate the gums, leading to gingivitis (the early stages of gum disease), periodontitis (the later stages of gum disease), or it can start to dissolve the teeth, leading to tooth decay.
When plaque is not properly removed, either due to improper hygiene technique or no hygiene at all, it builds up even further on teeth and starts to harden. All the minerals produced in saliva which normally protects against the tooth against the decay precipitates on hardens the plaque on the teeth. This is when it becomes tartar.
Tartar is firmly attached, almost like cement stuck to the teeth. This strong attachment means it is unable to be removed by toothbrushes! No matter how hard you brush, the tartar will remain, while excessive toothbrushing can actually damage the gums. Sometimes, when tartar is stuck firmly below the gums, the hygienist will need to anaesthetise your gums in order to properly remove the tartar.
This is why regular visits to your regular dental hygienist is so important in order to maintain proper oral health! Hygienists can use specialised equipment to remove the tartar from teeth comfortably, to restore the health of your gums.