The cell that has a nucleus surrounded by a membrane and many other specialized organelles is called a eukaryotic cell.

Here's why:

* Nucleus: Eukaryotic cells have a true nucleus, a membrane-bound organelle that contains the cell's genetic material (DNA).

* Organelles: Eukaryotic cells are characterized by the presence of numerous membrane-bound organelles, each with a specific function. Examples include mitochondria (energy production), Golgi apparatus (protein processing), endoplasmic reticulum (protein synthesis and lipid metabolism), lysosomes (cellular digestion), and more.

In contrast, prokaryotic cells (like bacteria and archaea) lack a true nucleus and other membrane-bound organelles. Their DNA is located in a region called the nucleoid, which is not enclosed by a membrane.