
rausnehmen
to take out
To remove something from a container, a place, or a larger whole.
Kannst du bitte die Milch aus dem Kühlschrank rausnehmen?
Can you please take the milk out of the fridge?
to take out / remove
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to take out
To remove something from a container, a place, or a larger whole.
Kannst du bitte die Milch aus dem Kühlschrank rausnehmen?
Can you please take the milk out of the fridge?

to remove
To remove or delete a part from a larger whole, such as a text, list, or plan.
Den letzten Absatz sollten wir besser rausnehmen, er passt nicht zum Rest des Artikels.
We should probably remove the last paragraph; it doesn't fit with the rest of the article.

to step back
To deliberately give oneself a break from an activity, obligation, or stressful situation.
Nach dem anstrengenden Projekt muss ich mich erstmal für ein paar Tage rausnehmen.
After the exhausting project, I need to step back for a few days first.

to take liberties
To presume or allow oneself to do something that is perceived as inappropriate or cheeky.
Er nimmt sich einfach raus, über alle anderen zu bestimmen.
He simply takes the liberty of deciding for everyone else.
'Rausnehmen' (to take out/remove) is a separable verb. In a main clause, the prefix 'raus' goes at the end. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Er nimmt den Kuchen aus dem Ofen raus.
He takes the cake out of the oven.
The prefix 'raus-' is a common colloquial shortening of 'heraus-'. The verb 'herausnehmen' has the same meaning, but sounds more formal and is used more in written language.
Würden Sie bitte das Gepäck aus dem Fach herausnehmen?
Would you please remove the luggage from the compartment?
When the verb is used reflexively with 'sich', the meaning changes completely. It then no longer means removing an object, but refers to a person who takes a break or allows themselves to do something inappropriate.
Ich glaube, ich nehme mich für den Rest der Woche raus und kuriere meine Erkältung aus.
I think I'll step back for the rest of the week and recover from my cold.
In the meaning 'sich etwas anmaßen' (to presume/to take liberties), a dative construction is used: 'sich (dative) etwas (accusative) rausnehmen'. The person doing the action is in the dative.
Was nimmst du dir eigentlich raus, so mit mir zu sprechen?
Who do you think you are, speaking to me like that?
to remove
With one item in a list or plan, both verbs can work. „Entfernen“ generally describes the fact that the item is no longer there afterward. „Rausnehmen“ emphasizes more strongly that a single item is taken out of a larger whole.

Ich nehme den alten Punkt aus dem Plan raus.
I take the old item out of the plan.
Ich entferne den alten Punkt aus dem Plan.
I remove the old item from the plan.