Place the potatoes into a saucepan of boiling salted water and boil for seven minutes, then drain and leave to cool.
When the potatoes are cool enough to handle, peel them and grate them into a bowl.
Add the grated beetroot and garlic, season, to taste, with salt and freshly ground black pepper, and mix together well.
Divide and shape the potato mixture into six flat patties, place onto a baking sheet and transfer to the fridge to chill for one hour.
Heat the oil in a large frying pan over a medium-high heat. Add the potato röstis and fry for 4-6 minutes on each side, or until golden-brown all over, then drain on kitchen paper.
For the horseradish sauce, mix the horseradish, crème fraîche and lemon juice together in a clean bowl and season, to taste, with salt and freshly ground black pepper.
To serve, place each rösti onto a plate. Top with a spoonful of horseradish sauce and a piece of salmon, then finish each plate with some sprigs of dill and a lemon wedge.