To determine which two perfect squares \(\sqrt{300}\) lies between, we should find the perfect squares closest to 300.
- The perfect square just below 300 is \(17^2 = 289\).
- The perfect square just above 300 is \(18^2 = 324\).
Since \(\sqrt{300}\) lies between \(\sqrt{289}\) and \(\sqrt{324}\), the answer is between 289 and 324.
So the correct response is:
289 and 324.