
zusehen
to watch
To follow or observe with your eyes what is happening, often without intervening yourself.
Wir sahen vom Fenster aus zu, wie die Kinder im Schnee spielten.
We watched from the window as the children played in the snow.
to watch / to make sure
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to watch
To follow or observe with your eyes what is happening, often without intervening yourself.
Wir sahen vom Fenster aus zu, wie die Kinder im Schnee spielten.
We watched from the window as the children played in the snow.

to make sure that
To ensure or see to it that something specific happens or is done in a certain way.
Sieh bitte zu, dass die Tür abgeschlossen ist, wenn du gehst.
Please make sure that the door is locked when you leave.
'Zusehen' (to watch/to make sure) is a separable verb. In a main clause, the prefix 'zu' comes at the end. In the infinitive with 'zu', 'zuzusehen' is written as one word.
Ich sehe dir gerne beim Kochen zu.
I like watching you cook.
When you watch a person doing something, that person is in the dative. You say 'Ich sehe dir zu' (I am watching you), not 'Ich sehe dich zu'.
Kann ich Ihnen bei der Arbeit zusehen?
Can I watch you work?
In the meaning 'dafür sorgen' (to make sure), 'zusehen' is almost always used with a subordinate clause that begins with 'dass' (that). The verb 'zusehen' comes directly before the comma.
Ich sehe zu, dass ich morgen alle E-Mails beantworte.
I will make sure that I answer all emails tomorrow.
In the imperative, 'Sieh zu, dass...' is often used as a colloquial, slightly urgent instruction to make sure that something gets done.
Sieh zu, dass du den Zug nicht verpasst!
Make sure you don't miss the train!
to look / watch
Schauen can directly name an event or media object being watched. Zusehen, by contrast, emphasizes that someone is observing what another person is doing, often without intervening. It therefore frequently takes a person in the dative or a subordinate clause.

Ich sehe heute meinem Bruder beim Fußballtraining zu.
I’m watching my brother at football practice today.
Ich schaue heute das Fußballtraining.
I’m watching football practice today.