How do you say, "I am also going to sleep" in German?
Ich werde auch schlafen oder Ich bin auch zu schlafen gehe?

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Ich werde auch schlafen. (possible, but unusual)
Ich werde (!) auch schlafen gehen.
Ich gehe (jetzt) auch schlafen.

There's a tendency in German to replace future with present if it is obvious from the context or construction (gehen + verb) that the action will take place in the future. Also note that "gehen + infinitive" is a special construction (go to some place and then start doing something) and not the same as "going to do s.th." in English. Also, "schlafen gehen" is a very common combination.

Answer

Another possiblity: "Ich gehe auch ins Bett".

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