Final answer:
King George III agreed to grant American independence following the American victory at the Battle of Yorktown. This decisive battle led to the end of the Revolutionary War and the signing of the Treaty of Paris.
Step-by-step explanation:
King George III agreed to give the Americans their freedom after the victory at a) Battle of Yorktown. The American victory at the Battle of Saratoga was a major turning point in the American Revolutionary War, convincing France to recognize American independence and form a military alliance. However, it was the defeat of the British by American and French forces at the Battle of Yorktown that led to the end of the war. British General Cornwallis surrendered at Yorktown, and following this defeat, Britain voted to end military operations and begin peace negotiations, culminating in the Treaty of Paris which formally recognized American independence.