The site of ribosome synthesis inside the nucleus is called the nucleolus.

Here's a breakdown:

* Nucleolus: This is a dense, spherical structure within the nucleus.

* Ribosome synthesis: The nucleolus is responsible for producing ribosomal RNA (rRNA) and assembling the ribosomal subunits.

* Ribosomal subunits: These are the two main components of a ribosome (the large and small subunits). They are assembled in the nucleolus and then exported to the cytoplasm, where they combine to form functional ribosomes.

So, the nucleolus is the "factory" within the nucleus that produces the essential components of ribosomes.