The king claudius tells rosencrantz and guilderstern that he is glad to see them but he needed their service to find out what ?

He needed their service to find out the reason behind Hamlet's melancholy.

Explanation:

Hamlet is extremely angry at his uncle, Claudius, because he murdered Hamlet's father. Hamlet thus decides to act as a mad man to take revenge on him.

Claudius has noticed 'a change' in Hamlet's behavior, but does not know the real reason behind it. In Act II, Scene II, Claudius and Gertrude welcome  Rosencrantz and Guildenstern, Hamlet’s friends. Concerned about Hamlet's behavior after his father's death, the king hopes that Hamlet's friends will help him overcome this hard period, or at least find out the real reason behind his melancholy. Claudius invites them to spend some time at court with Hamlet and discover if there is any particular problem that he is facing. Rosencrantz and Guildenstern agree to help.

to me i think class room sitting education is better. i do online school and i have not learned a think haha. when i sit in the classroom i just sit there and kind of pay attention but still i get so far ahead in the class when im doing online i have nothing else better to do but play video games and i sit in school and learn and have friends and just actually learn. when i'm doing online i sit here listing to music and get on and and look up the answers i guess that is my fault for being a cheater. but to be honest i think sitting in the classroom is better.