This is the 34th most frequent Slovak word.
slovensku
"Slovensku" means "Slovakia" in the dative or locative case in Slovak.
Here, 'na Slovensku' indicates the use of the locative case, denoting the location where the action is happening.
Cestujem na Slovensku.
I am traveling in Slovakia.
The phrase 'na Slovensku' in this context highlights the locality where the fame of the castle is recognized, employing the locative case.
Tento hrad je na Slovensku veľmi známy.
This castle is very famous in Slovakia.
In this example, 'na Slovensku' again uses the locative case, describing where the traditional music is enjoyed.