Final answer:
The priority action for a patient with diabetic ketoacidosis, high blood sugar, and low serum potassium is to place them on a cardiac monitor to prevent life-threatening arrhythmias while preparing for further treatment, such as potassium and insulin administration.
Step-by-step explanation:
The patient with diabetic ketoacidosis (DKA) presents with a very high serum glucose level and low serum potassium level. In diabetic ketoacidosis, insulin therapy is crucial for reducing high blood sugar levels; however, administering insulin can further lower serum potassium. As serum potassium is essential for proper cardiac function, monitoring the cardiac rhythm is the priority to prevent life-threatening arrhythmias.
Therefore, the correct action prescribed by the healthcare provider that the nurse should take first is to place the patient on a cardiac monitor. This is to ensure the patient's heart rhythm and function are closely observed while subsequent treatments, such as administering IV potassium supplements and starting insulin infusion, are provided as needed and in a controlled manner.