reinschauen
to drop by
Colloquial for visiting someone briefly and informally or stopping by a place for a short time.
Ich schaue später noch kurz bei dir rein, um das Buch abzuholen.
I'll drop by your place briefly later to pick up the book.

to drop by / look in
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to drop by
Colloquial for visiting someone briefly and informally or stopping by a place for a short time.
Ich schaue später noch kurz bei dir rein, um das Buch abzuholen.
I'll drop by your place briefly later to pick up the book.

'Reinschauen' (to drop by / look in) is a separable verb. The prefix 'rein' comes at the end in main clauses. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Schau doch mal kurz bei mir rein!
Do drop by my place for a moment!
'Reinschauen' (to drop by / look in) is the colloquial short form of 'hereinschauen'. It is mainly used in spoken, informal language.
Wenn du Zeit hast, schau doch mal auf einen Kaffee rein.
If you have time, drop by for a coffee.
The preposition in the sentence helps you recognize the meaning. 'Bei jemandem reinschauen' means to visit someone, while 'in etwas reinschauen' means to look into something or watch something.
Ich schaue später bei meinen Großeltern rein.
I'll drop by my grandparents' place later.
When 'reinschauen' (to drop by) means a short visit, the person you are visiting usually appears with the preposition 'bei' plus the dative.
Sollen wir auf dem Rückweg noch bei Anna reinschauen?
Should we drop by Anna's place on the way back?
to look at / to watch
'ansehen' and 'reinschauen' can both have to do with looking or watching. 'ansehen' is neutral and means that you look at something or, for example, watch a film. 'reinschauen' is more colloquial and often shorter or less committed. You can 'in eine Tasche reinschauen' (look inside a bag), meaning look into it, or briefly 'in eine Sendung reinschauen' (watch a bit of a show). The words can be confused because both can fit with media or with looking at something. 'ansehen' sounds more precise when you look at something deliberately and completely. 'reinschauen' sounds more like checking briefly or starting to watch something for a short time.

Ich schaue später kurz in das Video rein, wenn ich Zeit habe.
I'll take a quick look at the video later when I have time.
Zur Vorbereitung sieht sich die Ärztin die alten Befunde noch einmal an.
To prepare, the doctor looks at the old findings again.