Learn Hardcore Icelandic: Geturðu lagað snjallsímann minn?

It’s getur (2nd person singular of geta = can) + þú compressed into the clitic -ðu: getur þú → geturðu. In speech and informal writing, these are commonly written together. You’ll also see similar fusions like ertu (from ert þú) and veistu (from veist þú). Using the separated form Getur þú … ? is also correct and a bit more formal or emphatic.

Why is it lagað and not laga after Geturðu?

With geta (can), Icelandic uses the supine form (often identical to the neuter past participle), not the infinitive. So you get: ég get gert, geturðu hjálpað, getum við séð, and here geturðu lagað. You also don’t use að here—geturðu að laga is incorrect.

What case is snjallsímann, and why does it end in -nn?

It’s the definite accusative singular of snjallsími (smartphone). Laga takes a direct object in the accusative, and because the possessive comes after the noun, the noun also gets the suffixed definite article. Definite singular forms:

Nom: snjallsíminn
Acc: snjallsímann
Dat: snjallsímanum
Gen: snjallsímans

Why do we say snjallsímann minn instead of just snjallsími minn? Isn’t the possessive already making it definite?

In Icelandic, when a possessive pronoun is placed after the noun (postposed), the noun normally also takes the suffixed definite article: bíllinn minn, hundurinn minn, snjallsímann minn. This is called “double definiteness.” If you put the possessive before the noun, you drop the article: minn snjallsími. The preposed version is possible but is usually more emphatic, literary, or used in set phrases. A few kinship words are exceptions (e.g., mamma mín without the article), but snjallsími is not one of them.

Does minn have to agree with snjallsími? What are the other forms?

Yes. Possessives like minn/þinn/sinn agree with the noun in gender, number, and case. Snjallsími is masculine singular. Examples:

Nom: snjallsíminn minn
Acc: snjallsímann minn
Dat: snjallsímanum mínum
Gen: snjallsímans míns

Do I have to say snjallsími? Would just sími work?

Sími by itself commonly means “phone,” and in everyday speech it usually refers to a smartphone. So Geturðu lagað símann minn? is perfectly natural. Snjallsími is used when you want to be explicit (e.g., in technical or formal contexts).

Is Geturðu … ? polite enough? How can I make it more polite or softer?

Geturðu … ? is neutral and fine with people you know. To sound softer/more polite:

Gætirðu lagað … ? = Could you fix … ? (uses the past subjunctive gætir, more tentative)
Myndirðu geta lagað … ? = Would you be able to fix … ?
Add vinsamlegast (please): Geturðu vinsamlegast lagað … ? or Gætirðu vinsamlegast lagað … ?

How do I ask this to staff at a shop (plural you)?

Use the plural forms:

Getið þið lagað símann minn? (Can you [pl] fix my phone?)
More polite: Gætuð þið lagað símann minn? or Mynduð þið geta lagað símann minn?

Any pronunciation tips for this sentence?

ð in Geturðu and lagað is like the th in English “this.”
j is like English “y”: snj- ≈ “sny-”.
ll is pronounced roughly like “tl” (or “dl,” depending on dialect): snjall- ≈ “snyatl-”.
Main stress is on the first syllable of each word: GE-tur-ðu LA-gað SNJALL-sí-mann MINN.

Could I use gera við instead of laga?

Yes. Gera við is a very common verb phrase for repairing physical things. You could say Geturðu gert við símann minn? Nuance:

laga = fix, adjust, improve (general)
gera við = repair (specifically for broken items)

Where does ekki go if I want to say “Can’t you fix my smartphone?”

Place ekki after the finite verb (and any attached clitic): Geturðu ekki lagað símann minn? Not: Geturðu lagað ekki …

What pronoun would replace snjallsími later in the conversation?

Snjallsími/sími is masculine, so use hann (him/it): Já, ég get lagað hann = “Yes, I can fix it.”

Why does the verb come first? Could I say Þú getur lagað símann minn? as a question?

Yes/no questions in Icelandic typically put the finite verb first: Geturðu … ?, Ertu … ? Saying Þú getur lagað símann minn? with rising intonation can work in informal speech (often to confirm something you think is true), but the standard neutral question uses verb-first order.