Question: > 
> the blue-eyed girl
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> 
> 

This English construction can be rendered into German as either of the following:

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> Das Mädchen mit den blauen Augen.
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> Das Mädchen, das blaue Augen hat.
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But is there any way of saying that similar to the English construction: *adjective + adjectivized noun* [*blue-eyed*]?

Answer: 
The shortest is:

> 
> Das [blauäugige](http://www.duden.de/rechtschreibung/blauaeugig "Duden: blauäugig") Mädchen.
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In German there is exactly this construction (adjective + adjectivized noun), but we don't need a hyphen for it. I even guess, that this construction is even more often used in German than in English:

> 
> das blauäugige Mädchen  
> 
>  the blue-eyed girl
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> 
> der dunkelhaarige Mann  
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>  The dark-haired man
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> die langbeinige Frau  
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>  the long-legged woman
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> der breitschultrige Kerl  
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>  the wide-shouldered guy
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but also

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> das kurzärmelige Hemd  
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>  the short-armed shirt
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> das dünnwandige Glas  
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>  the thin-walled glass 
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and of course

> 
> der dickhäutige Elefant  
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>  the thick-skinned elephant 
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>