Should radiation be used on a thyroid if there has been no biopsy?

Yes in some cases: If you have graves' disease without any thyroid nodules, then a good treatment is radioactive iodine. If you have a hot nodule that was confirmed on a thyroid uptake and scan, then you don't need a biopsy prior to ablation. Otherwise, it's a case by case basis but there are cases (more common) where it is appropriate to ablate without a biopsy.