Question

Sparta finally was able to defeat Athens at the end of the Peloponnesian War after they

Answer 1

Destroyed Athens fleet.

A more detailed answer:

Finally, in 405 BC, at the Battle of Aegospotami , Lysander captured the Athenian fleet in the Hellespont. Lysander then sailed to Athens and closed off the Port of Piraeus. Athens was forced to surrender, and Sparta won the Peloponnesian War in 404 BC

OR:

The destruction of Athens's fleet in the Battle of Aegospotami effectively ended the war, and Athens surrendered in the following year. Corinth and Thebes demanded that Athens should be destroyed and all its citizens should be enslaved, but Sparta refused.

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-RosemaryAndStars