quadratisch
square
Having the shape of a square, with four sides of equal length and four right angles.
Für das Mosaik benötigen wir viele kleine quadratische Fliesen.
For the mosaic, we need lots of small square tiles.

square / quadratic
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square
Having the shape of a square, with four sides of equal length and four right angles.
Für das Mosaik benötigen wir viele kleine quadratische Fliesen.
For the mosaic, we need lots of small square tiles.

The adjective 'quadratisch' (square/quadratic) is derived directly from the noun 'das Quadrat' (the square). If you know the noun, you can easily work out the meaning of the adjective.
Der Raum hat eine quadratische Grundfläche.
The room has a square floor plan.
In its geometric meaning, 'quadratisch' (square) often describes the shape of everyday objects. Typical combinations are 'ein quadratischer Tisch' (a square table), 'ein quadratisches Zimmer' (a square room), or 'eine quadratische Form' (a square shape).
Wir haben einen praktischen, quadratischen Couchtisch gekauft.
We bought a practical, square coffee table.
You can recognize the mathematical meaning from signal words like 'Gleichung' (equation), 'Funktion' (function), or units of measurement like 'Meter' (meter). A 'Quadratmeter' (square meter) is an area of one meter by one meter.
Die Fläche des Zimmers beträgt zwanzig Quadratmeter.
The area of the room is twenty square meters.
The colloquial meaning 'praktisch, gut' (practical, good) comes from the well-known advertising slogan 'Quadratisch. Praktisch. Gut.' (Square. Practical. Good.) by the chocolate brand Ritter Sport. The usage is usually ironic or humorous.
Sein Lösungsvorschlag war einfach, aber quadratisch: Er hat das Problem perfekt gelöst.
His proposed solution was simple but square: it solved the problem perfectly.
good
'gut' and 'quadratisch' can both mean something positive in a special colloquial use. 'gut' is the normal and neutral word for quality. 'quadratisch' actually means a shape with four sides of equal length. Only in a casual expression, often as a reference to advertising, can it also mean 'practical, solid, and good'. For that reason, 'quadratisch' almost never directly replaces the word 'gut'. If you want to give clear, general praise, use 'gut'. 'Quadratisch' only fits in a playful or advertising-like style.

Frau Schneider nennt die kleine Box quadratisch, praktisch und gut.
Ms. Schneider calls the small box square, practical, and good.
Die Beratung im Büro war gut und hat mir sehr geholfen.
The consultation at the office was good and helped me a lot.