Thanks. That made me look at dict.cc (German English Online Dictionary) a bit more.
das Haus (noun) = House (We live in that blue house over there.)
das Zuhause (noun) = Home (Your home is warm and cozy.)
* Hause (as a noun) = * I can't find this word without 'zu', 'nach', or 'im' before it. But, any reference I find all relates to "home". I didn't find a gender for Hause, either. So, I don't believe this is a stand-alone German noun at all, just part of the adverbs 'zu Hause', 'nach Hause', 'im Hause'.
zu Hause / zuhouse (adverb) = home , at home
nach Hause / nachhause (adverb) = home , at home
im Hause (adverb) = indoors, about the house, on premises.
zu (proposition/dative) = to, too, at ['at' seems to be only applied when used with "home"]
nach (preposition/dative) = toward, to, on
To help answer fatuscat, "Why is the "zu" necessary?"
A: If I'm not mistaken, 'zu' is necessary because it is part of the adverb "zuhouse" or "zu House" (they are the same adverb to mean, 'home' or 'at home'). Since 'Hause' doesn't appear to be an actual German noun, it wouldn't make any sense to remove 'zu' from the adverb, 'zu Hause'/'zuhause'.
It seems that by breaking up the adverb "zuhause" into "zu Hause" (still an adverb) and capitalizing the "Hause" it kind of makes a pseudo preposition/noun.
Just don't look at "zu Hause" as two separate words or "Hause" as a noun....look at it as "zuhause". Same goes for "nach Hause" and "im Hause".
"because too many people are complaining" would be my guess, possibly in connection with "the person who edited this sentence to accept those doesn't speak English and/or German very well".
I can't see who last edited that sentence. Possibly it was the Pearson editors.
The translation into German also accepts da Heim which should, I think, be daheim.
Prepositions often have many meanings -- this is not limited to English or German.
As such, one preposition in one language will often translate to several prepositions in another language, but the "number of meanings" will probably be even larger than that, and difficult to count.
For example, perhaps von has 27 meanings; 13 of those correspond to 13 meanings of "of" and 5 of them to 5 meanings of "from", with the remaining 9 meanings corresponding to other expressions in English. (Just making up numbers to show that the number of translations is not really related to the number of meanings.)