radikal
radical
Fundamental, complete, and far-reaching. Often describes a change or solution that gets to the root of a problem.
Die neue Regierung plant eine radikale Steuerreform.
The new government is planning a radical tax reform.

radical
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radical
Fundamental, complete, and far-reaching. Often describes a change or solution that gets to the root of a problem.
Die neue Regierung plant eine radikale Steuerreform.
The new government is planning a radical tax reform.

The word 'radikal' (radical) comes from the Latin 'radix', meaning 'root'. A radical solution or change is therefore one that 'gets to the root' of a problem and addresses it fundamentally.
Er schlug eine radikale Vereinfachung der Bürokratie vor.
He proposed a radical simplification of the bureaucracy.
'Radikal' (radical) can be neutral ('fundamental') or negative ('extremist'). In connection with solutions, reforms, or changes, it is often neutral. In a political or social context, it more often has a negative connotation and describes uncompromising positions.
Die Firma plant eine radikale Umstrukturierung.
The company is planning a radical restructuring.
In the meaning 'fundamental', 'radikal' (radical) is often combined with nouns that describe a change. Common combinations are 'eine radikale Reform' (a radical reform), 'eine radikale Änderung' (a radical change), or 'ein radikaler Schnitt' (a radical cut/break).
Nach der Trennung entschied sie sich für einen radikalen Haarschnitt.
After the breakup, she decided to get a radical haircut.
The word family also includes the noun 'die Radikalität' (radicalism/radicality) and the verb 'sich radikalisieren' (to become radicalized). The verb in particular is often used in a political context to describe the development toward extreme views.
Man befürchtet, dass sich einige Jugendliche im Internet radikalisieren.
There are fears that some young people are becoming radicalized online.
extreme
'extrem' and 'radikal' can both mean that something is not moderate. That is why they are sometimes confused, especially when talking about opinions or political positions. 'extrem' generally describes a very high degree or a position at the outermost edge. It can also be used for weather, sports, stress, or danger. 'radikal', on the other hand, often means that something is fundamental and uncompromising, for example 'eine radikale Veränderung' (a radical change) or 'eine radikale politische Haltung' (a radical political stance). If you only want to say that something is very strong, 'extrem' fits. If it is about a deep break, a very harsh solution, or an uncompromising stance, 'radikal' is more precise.

Nach der Krise änderte die Firma ihre Strategie radikal.
After the crisis, the company radically changed its strategy.
Ihr Terminplan ist diese Woche extrem voll.
Her schedule is extremely full this week.