Final answer:
Ethan Allen and the Green Mountain Boys' capture of Fort Ticonderoga was significant because the artillery obtained there was critical in forcing the withdrawal of British troops from Boston in 1776.
Step-by-step explanation:
The significance of Ethan Allen and the Green Mountain Boys to the eradication of British troops from Boston involves the capture of Fort Ticonderoga. In May 1775, along with Colonel Benedict Arnold, they led an offensive that successfully took the fort in New York. The strategic value of this victory was immense because the heavy artillery captured at Ticonderoga, particularly cannons, were later transported and used by Continental forces to fortify the high grounds surrounding Boston. This mountain-sourced artillery was deployed by General George Washington to force the withdrawal of British troops from Boston in March 1776. Without the firepower secured by Ethan Allen and his militia, the siege of Boston may have been prolonged, and the British stronghold in the city might not have been undermined when it was. This was a crucial step in the American struggle for independence and showcased how a coordinated action by a group of determined rebels could have profound effects.