Final answer:
Beowulf's battle with Grendel ends in Beowulf's favor, where he defeats the monster by tearing off its arm, thus bringing peace to the Danes and enhancing his reputation as a hero.
Step-by-step explanation:
The outcome of Beowulf's battle with Grendel is a heroic victory for Beowulf. In the epic poem, Beowulf, a young warrior of the Geats, comes to the aid of Hrothgar, the king of the Danes, whose mead hall has been under attack by the monster Grendel. Beowulf confronts Grendel in a fierce battle and, using his incredible strength, manages to defeat the creature single-handedly by tearing off its arm, which leads to Grendel's death. The victory over Grendel brings peace to the kingdom of the Danes and earns Beowulf great honor and respect. This battle is a central moment in the poem and showcases Beowulf's strength and bravery as a hero.