In a recent lesson, we looked at the verbs ansprechen, aussprechen, vorsprechen, nachsprechen, besprechen, and versprechen. However, there are many verbs related to speaking that do not contain the verb sprechen. 

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The verb sich unterhalten refers in particular to the art of conversation. Here it stands alone, but you will often see the construction sich mit jemanden unterhalten. 

So kannst du auf natürliche Weise lernen, dich auf Deutsch zu unterhalten.

This is how you can naturally learn to converse in German.

Captions 10-11, Deutsch mit Eylin: Fragewörter

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The verb reden is interesting because it can be used for both serious and less serious conversations. In terms of prepositions, you'll often see über etwas reden ("to discuss something") or mit jemandem reden ("to talk with someone"), and if someone tells you Wir müssen reden ("We need to talk"), it could be very serious indeed.

Als Nächstes möchte ich über die Geschichte Berlins reden.

Next, I'd like to talk about the history of Berlin.

Caption 16, Bundesländer und ihre Rezepte: Bundesland Berlin

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Hast du nicht gesehen, wie sie die ganze Nacht mit dem Typen geredet hat?

Did you not see how she was talking to that guy all night?

Caption 22, Die Wohngemeinschaft: Die Verabredung

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The verb diskutieren is less ambiguous. Beware: it is stronger than "to discuss" in English and can even be translated as "to debate," "to dispute," or "to argue."

Am siebenundzwanzigsten Juli wollen sie das Thema im Gemeinderat diskutieren.

On the twenty-seventh of July they want to discuss the topic in the city council.

Caption 38, Online-Flashmob: "Bud-Spencer-Tunnel" in Gmünd

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The verb quatschen is quite informal, and refers to chatting or conversation that isn't restrained by time or formalities. You might remember that the noun der Quatsch means nonsense, but the use of quatschen doesn't necessarily mean that the topic is nonsense, just maybe not so serious or important. The verb plaudern has a similarly informal meaning, while the verb labern does indicate a lack of sense or importance. 

Ich dachte, wir quatschen mal eine Runde.

I thought we could chat for a bit.

Caption 2, Großstadtrevier: Nicht mit mir

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Was quatschen die da hinten?

What are they chattering about back there?

Caption 19, Nena: Besser geht's nicht

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Und auch ein bisschen, äh, die Spieler noch mal zu treffen, mit denen so ein bisschen zu plaudern...

And also to meet the players a little bit again, to chat with them a little bit...

Captions 44-45, Mercedes Benz: Michael Schumacher und Nico Rosberg bei der Nationalmannschaft

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Der laberte irgendwas von Blüten.

He was babbling something about blossoms.

Caption 62, Die Pfefferkörner: Endspurt

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Further Learning
You'll find many examples with these verbs on Yabla German. Make sure you review their conjugations as well.