"Check up" is a phrasal verb meaning to examine something.

But notice how a more advanced word like "examine" is much easier to say and remember with a few simple words.

The phrasal noun form is checkup. Phrasal nouns usually combine the words of a phrasal verb into a single word.

To hold out (to wait for something) becomes a holdout (someone waiting), for example.

Anyway, the study of phrasal verbs can get very complex, so I just like to keep things simple by saying there are two basic types of phrasal verbs:

1 . Phrasal verbs with an obvious connection to some physical action

2 . Phrasal verbs that just help you sound more conversational

Remembering this will help you "sort" them into different categories so you can understand and use phrasal verbs like natives.

Check up is an example of the second type.

There's no logical reason why "up" needs to be there as a doctor could look up, down, around, etc. when looking for problems with your body.

But since this formal, medical situation should feel a bit more comfortable to reduce any potential stress for the patient, the up is added to make the verb sound more informal, relaxed and conversational.

A mechanic checks your car for problems, but a doctor gives you a checkup.

Understand the difference?

Of course, you can also say that you're taking your car in for a checkup. But, again, this makes the action seem more comfortable and conversational, like a visit to the doctor's office.

Remember that the first type of phrasal verb is usually pretty easy to understand because its clearly describing a physical action.

You can pick something to select or choose it, but the direction is uncertain:

You'd pick a person to marry, pick a TV channel to watch, or pick an apple from a tree.

But when you pick up an item, there's a clear understanding of the direction the object is moving in.

I picked up the pencil. = I grabbed and lifted the pencil.

I picked up a new TV yesterday. = I bought a new TV yesterday. = I physically selected and bought a TV, and either I or someone else lifted it from some location and brought it here.

When there isn't an obvious reason for "up" - or any other preposition - in a phrasal verb, it's most likely just there to make the speech more natural and conversational:

Textbook, standard English: I cooked some dinner.

Conversational English: I cooked up some dinner.

Textbook, standard English: I cleaned my room.

Conversational English: I cleaned up my room.

Textbook, standard English: I wrote a report.

Conversational English: I wrote up a report.

Can you feel the difference?
It takes time to learn to use phrasal verbs like a native, but if you just remember this simple idea about the two types of phrasal verbs, you'll become better at using them much faster. :)