Well, first of all I would check if your opponent is in sparta grup, because they never surrender. If he isn't I would just write "good game" to point out that I find the game finished.
Should I ask?

Ooooh Sparta huh? Sounds like the group for me.
Seriously though, that's a tough one. Stuck being being Mr. Nice guy and suffering through the rest of the game or being Mr. Jerk and risk offending them.
You should not ask your opponent to resign. it is his right to play on even if it prolongs the game for you or frustrates you. There is a long post on When/If to resign. But bottom line you can not force your opponent to quit. Enjoy the winning the game

I had a great situation. I had a guy who was only up by a knight tell me that I am lost in the game and to resign. It pissed me off and I told him that it was bitchy of him to and that I didn't care how good he is. He disabled chat and a few moves later I manage to snag his rook and putting myself up in the game.

There is a story about Samuel Reshevsky playing a much older man. Sammy was down to basically his King against quite a few pieces. While the much older man was becoming very annoyed with this kid, he started moving faster, and faster. After a few more moves Sammy claimed a stalemate and the 1/2 point.
So is it annoying when your opponent wont resign when down a hopeless amount of material? To some yes. But you always have to take the human element into consideration :-)

One of my most recent games was a tournament game against a very strong player, he played badly in the opening, and kept complicating things until ultimatley he was down a rook. I expected him to resign (or better had been expecting him to resign for some time now) when I was a clean rook up; The point was that he made me play the endgame out to mate. This is all considering that he was at the time in perhaps in the top 100 strongest playes in this site, and im no pushover myself and even then, AFTER losing the rook he made me play the game out for about a month. I consider this super-inapropriate, that being said, there's really nothing anyone can do about it it's a player's right to play out a game untill mate, so all we can do is rant about it!

Conditional moves are a good suggestion -- not only will it help to speed the game up, but it will also subtly let your opponent know that they conclusion is foregone without having to be as rude as to ask for a resignation.

If the king was in the middle of the board and u do conditional moves, you would have to do 8! conditional moves or 1 guessing move (if your not premium) so unless its a forced move for the king conditional moves wont help alot

They won't necessarily speed him up, but they will speed you up. If your opponent's not being a jerk about it, and just wants to play it out, they'll likely make a number of moves in a sitting and if they don't have to wait on you that should help immensely. If they are being a jerk about it, you can probably count on waiting a full three days between moves -- conditional or not.

What's the rush? Savor the victory lol. As for the question posed, you would be severely violating chess etiquette as well as general manners to ask an opponent to resign. Just play it out and don't bother playing chess if you're short on time.
Do what ya like. Don't let society tell you what is right or wrong for you. Make your own decisions and if you don't like it, make another one next time.

Thanks for all of your responses. He did resign on his own without any prompting (unless he read this posting), so problem solved, and I have some good ideas for the next time it comes up.

Well, first of all I would check if your opponent is in sparta grup, because they never surrender. If he isn't I would just write "good game" to point out that I find the game finished.
everyone should see that movie "300" about the 300 Spartans standing up to the Persians led by Xerxes...sometimes if i want to get fired up for an online chess game i watch it....i have the dvd with the directors cut also...hey how about the fight scene agains the "immortals" !! and the "this is Sparta"!! scene...and ..."Spartans what is your profession"?... scene...but i digress...
If I'm in a tournament game, and I have very obviously won but the other player insists on playing it out, is it polite to ask for a resignation? I'm thinking no, but now I have this game where it's my king, queen, and one more pawn against only his king... just a matter of time. Except that with 3 days per move, it could be a very, very long time. Maybe 10 moves to walk the other pawn down and finish it... that's potentially a month.
So, what to do? I fear just by posting this question my opponent could read it and become offended, and I don't want to offend anyone...
Thanks