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How to use it
Vedieť + infinitive is “know how.” Vedieť, že … is “know that” — same verb, different frame.
In a sentence
vedieť + infinitive — know how
Viem plávať.
I know how to swim.
vedieť, že — know that
Viem, že prší.
I know that it's raining.
Other
Chcem vedieť kto s nami ide.
I want to know who's coming with us.
Chcem vedieť, kto s nami ostáva.
I want to know who's staying with us.
Examples from Tatoeba (CC BY 2.0 FR).
Source
Slovak National Corpus (SNK) ↗English gloss from the frequency publish path. Includes Tatoeba example sentences when present.
Full attribution on References.