Are sanskrit and tamil related

Sanskrit language is from Indo Iranian family, whereas Tamil is from Dravidian language family. So, they both have different roots.

Sanskrit and Dravidian language - Tamil have a same rising period so Tamil and Sanskrit have much common in them.

The word ‘Aaam’ means ‘yes’ in both Sanskrit and Tamil.

This phrase is common in both languages.
सम्पादित धन: (sampaadhitha dhanam ) - earned wealth சம்பாதித்த தனம் - (sampaadhitha dhanam) – earned wealth

Both have independent existence as well as lots of common words. So both languages are not related as such but have some similarities.