Why do we use "dried up" instead of just "dried"?

In this case, "up" is used to express that something is "complete" or done "completely".

Examples:

At a restaurant. Don't fill up on bread, otherwise you'll have no appetite when the entré comes.

Re: driving

Did you fill up the gas tank? I got $20 worth. (= No. I only got some gas(oline)/(petrol)).

Grammar note:

This kind of verb is called a phrasal verb. Phrasal verbs are verbs that are 1 part verb + 1 or 2 parts preposition. The result is usually an idiomatic expression or some deviation from the base.

With the word(particle) "up", the meaning does not always mean "completely" but in this case it does.

So, I hope this answers your question, and I haven't "used up" all of your time.

Good luck

The adverbial form up is often used with verbs as an intensifier to add strength to the meaning you want to convey.

• Used as an intensifier of the action of a verb: typed up a list.

(AHD)