Die vernünftige Lösung ist, heute zu Hause zu bleiben.

Because Lösung is a feminine noun in German: die Lösung.

Here, die is the nominative singular definite article because Die vernünftige Lösung is the subject of the sentence.

So:

• die Lösung = the solution
• die vernünftige Lösung = the sensible/reasonable solution

If the noun were masculine or neuter, the article would be different:

• der Plan
• das Problem

Because adjectives placed before a noun in German usually take an ending.

Here, vernünftig becomes vernünftige because it comes after the definite article die and describes the feminine singular noun Lösung.

So:

• vernünftig = reasonable, sensible
• die vernünftige Lösung = the sensible solution

This is called adjective inflection.

A few comparisons:

• die vernünftige Lösung
• der vernünftige Plan
• das vernünftige Verhalten

In all of those, the adjective gets an ending because it stands before the noun.

Because all nouns are capitalized in German.

So in this sentence:

• Lösung is a noun, so it is capitalized.
• heute is not a noun, so it is not capitalized.
• bleiben is an infinitive verb, so it is not capitalized here.

This is one of the most noticeable differences from English writing.

The comma introduces an infinitive clause: heute zu Hause zu bleiben.

German often uses a comma before an infinitive clause, especially when the clause depends on a noun or functions as the content of the statement. Here, the sentence is essentially saying:

• The sensible solution is this: to stay at home today.

So the comma separates the main clause from the infinitive construction.

Main clause:

• Die vernünftige Lösung ist

Infinitive clause:

• heute zu Hause zu bleiben

Because they belong to two completely different structures.

1. zu Hause
   This is a fixed expression meaning at home.

2. zu bleiben
   This is the normal zu + infinitive structure, meaning to stay.

So the two zu words are not doing the same job.

Breakdown:

• heute = today
• zu Hause = at home
• zu bleiben = to stay

So:

• heute zu Hause zu bleiben = to stay at home today

Because zu Hause means at home, while nach Hause means to home / homeward.

This sentence uses bleiben = to stay, so it describes a location, not movement toward a destination.

• zu Hause bleiben = to stay at home
• nach Hause gehen = to go home

So:

• heute zu Hause zu bleiben = staying at home today
• not nach Hause, because that would suggest movement toward home

Because in a zu + infinitive clause, the infinitive verb normally comes at the end.

So German puts all the other information first, and the infinitive verb closes the clause:

• heute = today
• zu Hause = at home
• zu bleiben = to stay

This end position is very normal in German subordinate and infinitive structures.

You can think of the whole last part as:

• heute zu Hause zu bleiben = to stay at home today

with bleiben placed at the end as expected.

It is an infinitive clause acting like a noun phrase.

In English, we can also do something similar:

• The best option is to wait.
• The sensible solution is to stay home today.

In the German sentence, heute zu Hause zu bleiben is the thing identified as the sensible solution.

So the structure is:

• Die vernünftige Lösung = subject
• ist = linking verb
• heute zu Hause zu bleiben = predicative infinitive phrase

In simpler terms: it tells us what the solution is.

Heute zu Hause is the more natural order here.

German adverbs often follow a rough tendency of putting time expressions before place expressions, especially in neutral word order:

• heute = time
• zu Hause = place

So:

• heute zu Hause zu bleiben = natural and standard

You may sometimes hear different orders for emphasis, but heute zu Hause is the normal choice in a basic sentence like this.

Traditionally and very commonly, yes: zu Hause.

That is the safest form for learners to use in a sentence like this:

• Ich bin zu Hause.
• Er bleibt heute zu Hause.

You may also encounter zuhause as an adverb in modern usage, but zu Hause is extremely common and fully standard. For a learner, writing zu Hause is a very good habit.

Yes, that is also possible.

• Die vernünftige Lösung ist, heute zu Hause zu bleiben.
• Die vernünftige Lösung ist es, heute zu Hause zu bleiben.

The version with es sounds a bit more explicit or slightly heavier, but both are grammatical.

In everyday German, the shorter version without es is very natural.

In this sentence, vernünftig means sensible, reasonable, or practical.

It is a very common everyday word. A native English speaker should usually think of it as:

• vernünftig = sensible / reasonable

So Die vernünftige Lösung means something like:

• the sensible solution
• the reasonable solution

It suggests that staying home is the smart, practical choice.

Yes.

Both are good English translations:

• to stay home
• to stay at home

German uses zu Hause bleiben, and English may express that either way depending on style and region.

So in this sentence:

• heute zu Hause zu bleiben = to stay home today
• also: to stay at home today

Both capture the German well.