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Beowulf boasted by saying that he wouldl fight Grendel without a weapon.
The favor that Beowulf asks of Hrothgar is to allow Beowulf and his men to be the only ones to fight Grendel. This will allow Beowulf to prove his worthiness as a warrior and a leader.
Beowulf and Grendel fight at Heorot, the great mead hall of King Hrothgar in Denmark. The battle takes place in the darkness of the night while the warriors are sleeping, and it is a fierce and brutal encounter.
Grendel tortured Hrothgar's men for 12 years before Beowulf arrived to fight him.
Hrothgar's men are brave enough to fight Grendel when Beowulf arrives from Geatland and offers to face the monster. They were initially hesitant and paralyzed by fear until Beowulf's arrival instilled them with hope and courage.
Beowulf and Hygelac were welcomed warmly at Heorot, King Hrothgar's mead-hall, by the warriors and attendants. Hrothgar and his people were impressed by Beowulf's confidence and bravery, especially after he volunteered to fight the monster Grendel to protect Heorot.
Beowulf's father Ecgtheow was a good friend of Hrothgar's. Long ago, Hrothergar saved Ecgtheow's life. Beowulf comes to repay his father's "debt" to Hrothgar. This is the 'technical' reason he helps Hrothgar. Really though, Beowulf is a true hero. He seeks out a challenge, and Grendel is the ultimate challenge.
Yes, Beowulf gives Grendel's head and the hilt of the magic giant's sword to Hrothgar, and Hrothgar gives Beowulf treasure and gold, new golden chain mail, horses and weapons. Hrothgar also gives the men who sailed with Beowulf treasure-gifts. These treasures are given to Beowulf after both the fight with Grendel and the fight with Grendel's mother. After he defeats Grendel's mother, Beowulf sails home with his men and his treasures.
Once at Hrothgar's throne, Beowulf introduces himself as a hero who can crush water sprites, among other things. Therefore he is equipped to defeat Grendel, if Wyrd (or Fate) will have it so. Hrothgar welcomes Beowulf as the son of Ecgtheow, the man whom Hrothgar had helped in settling a feud with the Wylfingas long ago.
Beowulf boasted by saying that he wouldl fight Grendel without a weapon.
Beowulf and Grendel fought in the mead hall of Heorot, where Grendel had been terrorizing Hrothgar's warriors. The battle took place at night when Grendel attacked the hall, and Beowulf vowed to rid the hall of the monster.
Hrothgar didn't need Beowulf to fight him. Beowulf heard what was happening to his kingdom and came to help.