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Hello.

-It took ages to clean up the mess.
-It took ages to clean the mess.

Do to clean and to clean up have the same meaning ?
Do mess and dirt have the same meaning?

Thanks.
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In your sentences both work - clean/clean up.

Mess is not the same as dirt. Mess implies some kind of disorder whereas dirt is just dirt!

Tidy yourself up - you look a mess!
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Jesusengland-It took ages to clean up the mess.
-It took ages to clean the mess.

Do to clean and to clean up have the same meaning ?
They are more or less the same. However, I don't think I would say "clean a mess". You can clean a sink, clean a wall, clean a car, clean a floor, and so on -- any kind of object. You are making the sink, wall, car, or floor clean, by washing or polishing, or generally tidying the appearance of something, for example.

But you are not washing, polishing, or tidying the mess to make it clean. What you are cleaning is whatever the mess is covering. But you're cleaning up the mess.

CJ
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Hello.

But I can't understand well.

Why is it said "you're cleaning up the mess" and not "you're cleaning the mess"?

Thanks.
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An example of a mess is a clutter of papers and books on a table.
Cleaning is washing or polishing.
Are you taking each piece of paper and each book off the table and washing or polishing it and then placing back on the table? No. Therefore you are not cleaning the mess.
You are rearranging the papers and books so that they are more neatly stacked and ordered. You pick up (and set down) the papers and books in different positions until order is restored. You are tidying up, cleaning up (the mess).
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Another example of a mess is coffee spilled on the floor. The same logic applies. Are you taking the coffee off the floor and washing or polishing the coffee and putting it back onto the floor? No. So you are not cleaning the mess.
You use a cloth or sponge to absorb and pick up the spilled coffee. You are cleaning up (the mess).
You are cleaning the floor, but cleaning up the mess.

CJ
Hello.

So, is it wrong to say "to clean the hotel, room..." (instead of "to clean up the hotel, room)?

Thanks.