Learn Swedish: Skulle du låta taket isoleras istället för att byta kaklet? - Would you have the roof insulated instead of replacing the tiles?

This showcases the causative passive construction that this lesson focuses on. We use låta (to have/let) plus the object (taket) plus the passive infinitive (isoleras) to mean you are having a service performed on the object by an unnamed third party. If you used the active infinitive isolera, it would literally mean you were letting the roof insulate something else!

I learned that låta means 'to let' or 'to sound'. How does it translate to 'to have something done' here?

While låta often means 'to let' (give permission) or 'to sound', when it is paired with an object and another verb it acts as a causative verb. In this specific passive construction (låta + object + passive infinitive), it is the exact Swedish equivalent of the English structure 'to have [something] done' (arranged or commissioned) rather than just passively allowing it to happen.

English says 'instead of replacing' using an -ing word. Why does Swedish use att byta?

Swedish doesn't have a direct equivalent to the English -ing form (gerund) for this grammatical purpose. Instead, when a verb directly follows a preposition or prepositional phrase like istället för (instead of), Swedish requires the infinitive marker att followed by the infinitive verb (byta).

What is the base form of kaklet and why does it seem to drop a letter?