To think dentist is liable ?

[Lineem]

So I had a tooth extraction. It took a while as the tooth broke but dentist was sure it was all out in the end. Cost an arm and a leg.

2 weeks later , I’m in more pain than I was initially and went back to the same dentist. Turns out after an X-ray that part of the tooth was still in there.

Who should pay the cost of another extraction and X-ray ? Myself or the dentist ?

I would like to think not for another full extraction cost.
I wonder would you be liable for say..... an x-ray to check the situation?

If he's charged your for the extraction, then surely he needs to fully extract it?
Something similar happened to me but he knew it had gone wrong so he didn't chage me at all. It ubsequently caused me loads of problems.but he told me that I'd need to sort it out privately.
As it happened I changed dentist and they sent me to the hospital and I had it sorted on the nhs.
I'd definitely put the onus back on the dentist.

He needs to treat it until the initial, paid for treatment is complete.

I noticed recently that my NHS dentist charges once for a treatment no matter how many times you have to go back until it is fully complete. They obvs try to get it right first time, but eg if the filling hasn't settled they will fix it without charging again.

I would think that since he didn't fully extract the tooth the first time that you wouldn't have to pay anything because he didn't do the job correctly.

I paid for the X-ray and extraction initially and was charged again this time a surgical extraction (which is more expensive) due to his fault and the x Ray.
it’s a private dentist as couldn’t get an emergency NHS appointment and not entitled to a regular NHS dentist.

I would imagine at some stage you had been told there was a risk the tooth could break off ( probably other stuff too like infection or dry socket). Just because the tooth broke doesn't necessarily mean the dentist has done anything wrong. This applies to leaving a bit behind too. Of course they could have been at fault but it'll be impossible to prove.
You've now had a surgical extraction which is a different process. I bet you were offered a surgical extraction too inititially as they have no way of knowing if first procedure will work.
I'm afraid it looks like you need to pay

Did the dentist warn you of risk of tooth fracture and further procedures may be necessary if it happens? That’s a fairly typical warning for any tooth extraction. Did the dentist spend time with you attempting to extract your decayed tooth? Should they be paid for that time?

Noted PPs referring to dentist as ‘he’ after your first post where you didn’t say either way he or she!

You should cover the cost of the dentist’s time and materials so far, and the further cost of your own treatment

the tooth must have been in poor condition for it to have been extracted (it's really a rarity in my experience), with this in mind, complications can happen.
i would expect to have to pay but would secretly hope for some sort of reduced fee.

No my dentist didn’t mention it could break until he began and it started breaking. Many swear words later from him , he got it out and said it broke but he’s sure it’s all out or so he thought he did.

Dry socket and infection was never mentioned, even in the aftercare leaflet. I don’t even think I’d be able to tell if I had a dry socket as I don’t know the signs.

My issue is that I paid the full cost and then even more , no reduced fee - full consultation, X-ray and surgical extraction paid for. £600 in total.

If a plumber quoted me that it was going to be 3,000 for a new boiler, the fitting and cleaning of pipes, etc, that's what I'd expect to pay. If it then turned out that they hadn't done the job I'd paid them for, I'd expect them to come and rectify it for free.

I'm not sure why dentists would be any different. They're the experts. They examine you and give you a price. To charge for an x-ray to prove they hadn't done a proper job is so beyond cheeky.

When you put it like that , yes it’s my fault the tooth was bad but I didn’t pay for it to be half removed.

64hrs in work it takes for me to make up what I spent at the dentist

If a plumber quoted you to replace your boiler and it turned out your pipes were corroded and you needed more work than anticipated- you would have to pay for everything you needed. The plumber won’t do the additional work you need for free if the job is more complicated.

Its not the same. If I wanted just my boiler to be changed and I paid for that, and it later turned out the pipes were corroded, that's two separate jobs. Paying for the pipes to be replaced is a whole other job.
But if I paid for the boiler to be changed, and the whole system to be flushed through, I'd expect the plumber to notice the corroded pipes. If he then didn't tell me and flushed out the system, knowing that it would be clogging up again, I wouldn't expect him to charge me to come back and inspect the pipes. I obviously would accept paying extra for the pipes to be changed, but I'd expect him to stand the price of flushing the radiators again because it was his fault exposing me to the inevitable problems I would be facing.

It is the same. There’s a fee for a simple extraction. There’s a risk a rotten tooth will crumble and it will become a surgical extraction. That is a more complex procedure with a higher fee.
There’s a risk any task we ask a professional to do for us becomes more complex - plumber, solicitor, surgeon.
The dentist didn’t put the decay there - the cause of OPs problem. The dentist attempted to remove the tooth. The tooth fractured and the dentist attempted to remove all the fragments. OP returns in pain - dentist investigates cause of pain and makes plan for subsequent necessary procedure.
They haven’t done anything wrong- on the face of it.
If you didn’t sign a consent form that warned you of risks of tooth fracture OP perhaps they have done something wrong in not preparing you for this possibility, but the outcome would have been the same.

Sorry, but the dentist is in the wrong. They removed some of the tooth and they didn't even check if they'd got it all. Instead they sent their client away with a portion of tooth still remaining. They left the client in pain and they even expect her to pay for an x-ray to check that they hadn't done a proper job.