Robert210

Morning All I was hoping to get some advice on a problematic tree root which has pushed through our 6" concrete driveway which now causes problems for smaller cars to get over. I decided to dig around the root to help identify how large it was below ground and I have included photos as reference. My question is, If the whole tree root was to be removed, would it have a detrimental effect on the tree? (i.e death?) and secondly, would it make the tree vulnerable to falling? My other problem is that the smaller roots that have branched off are heading for my neighbour's driveway, therefore, would these be okay to cut off if we are safer leaving the large root in as we can live with that if it means saving the tree. I hope there is someone who can help and thank you all in advance for any advice received. Regards Robert