ausschauen
to look
To have a certain appearance or give a certain impression. Used especially in southern Germany and Austria.
Mit dem neuen Haarschnitt schaust du wirklich gut aus.
You look really good with the new haircut.

to look / to look out
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to look
To have a certain appearance or give a certain impression. Used especially in southern Germany and Austria.
Mit dem neuen Haarschnitt schaust du wirklich gut aus.
You look really good with the new haircut.

'Ausschauen' is a separable verb with the prefix 'aus-'. In a main clause, 'aus' goes at the end of the sentence.
Du schaust heute aber müde aus.
You look pretty tired today.
In the meaning 'aussehen' (to look), 'ausschauen' is used especially in southern Germany, Austria, and Switzerland. In other regions of Germany, you hear it less often.
Wie schaut's aus? Schaffen wir den Zug noch?
How does it look? Will we still make the train?
When 'ausschauen' means 'aussehen' (to look), it is almost always combined with an adjective or adverb that describes the condition or appearance.
Das Kleid schaut an dir fantastisch aus.
That dress looks fantastic on you.
The phrase 'Ausschau halten nach' (to look out for) is a fixed combination. Here, 'Ausschau' is a noun. The preposition 'nach' always takes the dative.
Halte bitte nach einem freien Parkplatz Ausschau.
Please look out for a free parking space.
to shine / seem
'scheinen' and 'ausschauen' can both describe how something comes across to someone. 'scheinen' is general and means that you have an impression that may not be completely certain. It can be about appearance, behavior, or a situation. 'ausschauen' mainly means 'to look' or 'to give a certain impression' and is especially common in southern Germany and Austria. The words can be confused when you want to say how someone or something seems. In standard German across regions, 'scheinen' is often more neutral; 'ausschauen' sounds more regional and more strongly connected to outward appearance.

Nach dem langen Arbeitstag schaut Max ziemlich müde aus.
After the long workday, Max looks pretty tired.
Der Plan scheint gut zu funktionieren.
The plan seems to be working well.