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In the following sentence:
Но насколько на самом деле опасна радиация?
This sentence does not seem to work if I use опасная (long form). I checked the rule for long/short forms, but both forms seem to work. I'm not usin any complement to the adjective (like готов к экзамену) nor am I using any infinite verb (like намерен выполнить всё), so I thought both forms work.
But why is опасная not correct here?
One could discuss the stylistic norms of long vs. short adjectives at length, but the biggest problem here I think is that the long form creates a clarity issue. Опасная immediately followed by радиация parses naturally as a noun phrase, so extra effort is needed to realise that this is "but how dangerous is the radiation really?" and not an incomplete sentence along the lines of "but how much does/is the dangerous radiation really [...]?". A "the old man the boats" kind of situation.
You need to use the short form of an adjective when it functions as a verb ("сказуемое", maybe "predicate" is the correct English term).
Радиация (что делает?) опасна.
Радиация суть опасна but modern Russian just drops the verb there.
The way I see it, the full form of adjectives signifies some kind of permanent, unalienable property, while the short form may mean the property is under assession or doubt.
Thus, as Nikolay Ershov said, опасная радиация would be parsed as a noun phrase.
For instance, "он тогда был плох" would mean he was ill (bad) at the time, while "он тогда был плохой" would mean he was a bad guy.
So, the full form is like adding an article in English: "he was a bad" vs "he was bad". So, "Но насколько на самом деле опасная радиация?" reads like "How much a/the dangerous radiation?", and reads, as stated previously, like a noun phrase.
«Насколько» is the complement.
