My crown just came out. my dentist says the root needs to be extracted. does that mean immediately? as in tomorrow? or can it wait a week?

Likely can wait: Is there an infection, are you in pain? If not , it can most like wait a week, but don't put it off too long. Avoiding treatment tends to lead to more complications.

It depends: If there is infection, it needs to be treated first.

No: If therte is not much pain, you can wait.

Extract vs Infect: It would most likely be best not to wait to prevent potential of infection. Discuss with your dentist options you have for a tooth replacement. If the both of you decide on a implant (ideal), the decision needs to be made if the implant can be placed at the same time as the extraction or if a bone graft (socket preservation) may be needed before a implant can be placed.

Ask your DDS: That is a question only your dentist can answer accurately as he or she is aware of exactly the conditions present and the likelihood of problems if you wait.

Pain? Swelling?: Infection? More info would be needed to assess the condition of the tooth. Even without any of the above symptoms, the problem can escalate overnight. Discuss your concerns with your dentist and the pros/cons of immediate vs delayed treatment. All the best...