Final answer:
The Visigoths asked permission to settle within the Roman Empire for various reasons, including seeking a safe place, utilizing the resources, and maintaining a diplomatic relationship.
Step-by-step explanation:
The Visigoths asked permission to settle within the Roman Empire for various reasons. One reason was that the Visigoths were facing pressure from the Umayyad Caliphate and needed a safe place to establish a kingdom. By settling within the Roman Empire, they could benefit from the established infrastructure and resources. Additionally, by seeking permission, the Visigoths attempted to maintain a diplomatic relationship with the Roman Empire, which could provide military support and protection.