"Ей нужен размер поменьше."
Translation:She needs a smaller size.
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2074
Because it matches размер. With нужен, the object needed is in the nominative and the person who needs is in the dative case.
1362
This: https://en.wikipedia.org/wiki/Grammatical_case Which is Russian looks like that: https://ru.wiktionary.org/wiki/%D0%BE%D0%BD%D0%B0#.D0.A0.D1.83.D1.81.D1.81.D0.BA.D0.B8.D0.B9
1362
But English has 2 (3) cases, while Russian has 7. Of course Russian will distinguish things that English doesn't. Also, I have never in my life seen any two languages whose cases are identical in function. The mistake you are making here is thinking you can translate one English structure into an equivalent Russian one. You can't. You have to make another one. This structure here actually goes along the lines “To here [Dat] • (is) needed • size [Acc] • little-smaller“. Grammatically speaking, it's the same structure as English “I am writing a letter [Acc] to her [Dat]”.