sorglos
carefree
Without worries, fears, or concerns; lighthearted and unworried.
Die Kinder spielten den ganzen Nachmittag sorglos im Garten.
The children played carefree in the garden all afternoon.

carefree / careless
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carefree
Without worries, fears, or concerns; lighthearted and unworried.
Die Kinder spielten den ganzen Nachmittag sorglos im Garten.
The children played carefree in the garden all afternoon.

The word is made up of 'Sorge' (worry) and the suffix '-los' (-less). The suffix '-los' means 'without', so 'sorglos' literally means 'without worries'. This pattern appears in many words such as 'arbeitslos' (unemployed) or 'hoffnungslos' (hopeless).
Nach der bestandenen Prüfung fühlte er sich frei und sorglos.
After passing the exam, he felt free and carefree.
The meaning of 'sorglos' (carefree / careless) depends strongly on the context. If it refers to a phase of life or a state of mind (e.g., childhood, vacation), it has a positive meaning. If it refers to handling something or to behavior, it is often negative in the sense of 'fahrlässig' (negligent).
Sie erinnert sich gern an ihre sorglose Jugend auf dem Land.
She likes to remember her carefree youth in the countryside.
In the positive meaning 'unbeschwert' (carefree), 'sorglos' is often connected with periods of time or a feeling about life. Typical phrases are 'eine sorglose Kindheit' (a carefree childhood), 'sorglose Tage' (carefree days), or 'ein sorgloses Leben' (a carefree life).
Wir verbrachten ein paar sorglose Tage am Meer.
We spent a few carefree days by the sea.
In the negative meaning 'fahrlässig' (negligent), 'sorglos' usually describes an action or behavior. A very common combination is 'der sorglose Umgang mit etwas' (the careless handling of something).
Der sorglose Umgang mit Chemikalien ist gefährlich.
Careless handling of chemicals is dangerous.
careful / cautious
'vorsichtig' and 'sorglos' can be opposites when talking about behavior in a situation. Someone who is 'vorsichtig' (careful / cautious) pays attention to possible problems and tries to avoid mistakes or damage. Someone who acts 'sorglos' does not think enough about risks or consequences. 'sorglos' can also have the positive meaning 'carefree', but in contrast to 'vorsichtig' it means something more like: too little attention or too little responsibility. So 'vorsichtig' is careful and thoughtful; 'sorglos' in this sense is careless.

Max ging sorglos mit den wichtigen Formularen um und verlor eines davon.
Max handled the important forms carelessly and lost one of them.
Beim Umzug trägt die Nachbarin die Glaslampe sehr vorsichtig.
During the move, the neighbor carries the glass lamp very carefully.