gründlich
thorough
Carried out carefully and with great precision; taking all details into account.
Vor dem Einzug haben wir die Wohnung gründlich geputzt.
Before moving in, we cleaned the apartment thoroughly.

thorough
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thorough
Carried out carefully and with great precision; taking all details into account.
Vor dem Einzug haben wir die Wohnung gründlich geputzt.
Before moving in, we cleaned the apartment thoroughly.

The adjective 'gründlich' (thorough) is related to the noun 'der Grund' (ground/reason). It describes an action that goes 'bis auf den Grund' (to the bottom), meaning it is very deep, detailed, and complete.
Eine gründliche Recherche ist die Grundlage für einen guten Artikel.
Thorough research is the basis for a good article.
'Gründlich' (thoroughly) is often combined with verbs that describe a careful action. Typical examples are: to examine, check, clean, or prepare something thoroughly.
Der Arzt hat den Patienten gründlich untersucht.
The doctor examined the patient thoroughly.
As an adverb, 'gründlich' (completely/thoroughly) can intensify a negative statement and then means 'entirely' or 'completely'. It is often used with verbs like 'sich irren' (to be mistaken), 'sich täuschen' (to be wrong/misjudge), or 'etwas satthaben' (to be fed up with something).
Ich habe seine Absichten gründlich missverstanden.
I completely misunderstood his intentions.
exact / precise
'genau' and 'gründlich' can both mean that you work carefully and watch out for mistakes. The difference is in the focus: 'genau' emphasizes that the result is precise and correct. 'gründlich' emphasizes that you take your time and check all important details. An answer can be 'genau' if it is exactly correct. A check or cleaning is 'gründlich' if nothing is left out.

Mehmet liest den Vertrag gründlich, bevor er ihn unterschreibt.
Mehmet reads the contract thoroughly before signing it.
Der Lehrer erklärt die Lösung heute sehr genau.
The teacher explains the solution very precisely today.