Tooth has two parts one which you see in the mouth is called the crown and the other half is in the bone which is known as the roots.
The part which remains inside should be removed as any residual infection in the tooth may flare up and cause pain.
Next Steps
Visit a dentist
Get the Xray done and extract the root piece.
Health Tips
Also enquire about the means to replace the tooth to be extracted before hand as there is treatment in which dentist can immediately place a DENTAL IMPLANT in the bone socket of recently extracted tooth provided there is no infection.