Jeg må bytte ut kniven på kjøkkenet.

Breakdown of Jeg må bytte ut kniven på kjøkkenet.

jeg
I
måtte
must
kjøkkenet
the kitchen
in
kniven
the knife
bytte ut
to replace
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Questions & Answers about Jeg må bytte ut kniven på kjøkkenet.

What does mean in this sentence?
is a modal auxiliary verb meaning must or have to. It expresses necessity or obligation. In Norwegian, a modal verb is followed by an infinitive, so is followed by bytte ut.
Why do we use bytte ut instead of just bytte?
Bytte ut is a compound verb that means to replace. Bytte alone means to exchange (swap one thing for another) but doesn’t carry the sense of replacing an old item with a new one. Adding ut gives that specific meaning.
How do I use the compound verb bytte ut in different tenses?

• Infinitive: å bytte ut
• With a modal: må bytte ut (as in Jeg må bytte ut kniven)
• Present tense: bytter ut (e.g. Jeg bytter ut kniven)
The prefix ut stays attached to bytte; you don’t split it or move it to the end of the clause like in German.

Why is kniven in its definite form instead of kniv?
In Norwegian you add a suffix for definite nouns. Kniven = kniv (knife) + -en (the). Here you refer to the knife in the kitchen, not just a knife, so you use the definite form.
Why do we say på kjøkkenet instead of i kjøkkenet to mean “in the kitchen”?

Norwegian often uses (on/at) with rooms and specific places:
på kjøkkenet = in the kitchen
på badet = in the bathroom
Using i kjøkkenet would sound odd when just stating location inside a room.

Can I drop Jeg as in English “Must replace the knife”?

No. Norwegian is not a pro-drop language like Spanish or Italian. You normally need the explicit subject pronoun:
Jeg må bytte ut kniven.

How would I turn the statement into a question (“Do I need to replace the knife in the kitchen?”)?

Invert the modal and the subject:
Må jeg bytte ut kniven på kjøkkenet?

Can I use trenger å or erstatte instead of må bytte ut?

Yes:
Jeg trenger å bytte ut kniven på kjøkkenet (trenger å = need to; softer than )
Jeg må erstatte kniven på kjøkkenet (erstatte = to replace; more formal)
All three convey a similar idea, but bytte ut + is very common in everyday speech.