Final answer:
Maximilien Robespierre was the extremist leader whose execution ended the radical state, marking the conclusion of the Reign of Terror during the French Revolution.
Step-by-step explanation:
The leader of the extremists whose execution marked the end of the radical state was Maximilien Robespierre. He was a key figure during the French Revolution, and under his leadership, the Committee of Public Safety enforced the Reign of Terror. Robespierre's rule was characterized by a harsh crackdown on dissidents, and it involved the use of the guillotine as a symbol of the revolution's punitive measures. This period led to the execution of thousands, including prominent figures like Marie Antoinette and Georges Danton. The Reign of Terror generated fear and instability within France and ultimately led to Robespierre's downfall. In July 1794, Robespierre was ousted by members of the National Convention, arrested, and subsequently executed by guillotine, bringing an end to his reign of terror.