Final answer:
Plato's 'Republic' was written around 380 BCE and is a seminal work in philosophy and political theory, discussing the concept of justice.
Step-by-step explanation:
The approximate date that Plato's Republic was written is in the latter part of the fourth century BCE, specifically around 380 BCE.
This timeline places its composition after the Peloponnesian War and during a time when Plato was establishing his own philosophical thoughts post the death of his mentor, Socrates.
The Republic is a critical work in Western philosophy and political theory, in which Plato, through the character of Socrates, explores the meaning of justice and examines the order and character of the just city-state as well as the just individual.