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Wir haben kein großes Bad.

I do not understand why there is -es at the and of großes. The original word is groß. I first thought it was genitive, but then I figure out it is not. Can you help me?

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Let's do it step by step. First, we decompose the sentence:

[Wir](subject, nominative)  [haben](verb)  [kein großes Bad.](accusative object)

Second, we look up the noun Bad and see that it is neuter.

Third, we consult the declension tables for the adjective groß, for example, at Wiktionary. There are three possibilities for neuter gender and accusative case:

  • strong declension: großes
  • weak declension: das große
  • mixed declension: ein großes

The indefinite pronoun kein is an article word similar to ein. Therefore, mixed declension is in place here, where kein is weakly declined and großes is strongly declined, i. e., kein großes Bad.

You can find more about the topic declension rules in this community wiki.

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Bad is in Akkusativ case here. Bad is neuter (das Bad).

Since you thought großes would be Genitiv (due to the -es ending), you seem to mix up the declension of nouns and adjectives. You might want to have a look at the declension of adjectives

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