Why can't a cell survive without a nucleus?

Hint: In eukaryotic species, the nucleus is a membrane-bound organelle that houses genetic material (DNA). By aiding transcription and replication activities, the nucleus contributes to the cell's stability. The nucleus is the biggest organelle within the cell, accounting for around a tenth of the total cell volume.
The nucleus is the cell's brain. It protects the genetic information. The nuclear envelope, also known as the Karyotheca, is made up of two nuclear membranes and nuclear pores, as well as nucleoplasm and nucleoid. The 'Brain of the Cell' is what it's called.

Complete answer:
Prokaryotes are single-celled organisms that lack organelles and other structures that adhere to the inner membrane. Prokaryotes are organisms that lack a nucleus and other organelles in their cells. Archaea and bacteria are two types of prokaryotes that are classed separately. They don't have a nucleus, but they do have a single chromosome, which is a circular piece of double-stranded DNA found in the cell's nucleoid area. DNA is arranged in a single loop in the nucleoid zone of the cell. To duplicate the cell, the DNA loop is repeated, and one copy travels to each side of the cell as part of binary fission. A single circular segment of DNA carries genetic material in prokaryotic cells. The cytoplasm is in intimate contact with the cell membrane, which is connected to DNA. Because there is no physical nucleus, only a concentration of DNA called a nucleoid, there is no encircling membrane.

Note:
The cytoskeleton of prokaryotes is more primitive than that of eukaryotes. Apart from actin and tubulin homologues, flagellin, the helically organised building-block of the flagellum, is one of the most important cytoskeletal proteins in bacteria. Prokaryotes are frequently found in intracellular structures that can be exploited as primitive organelles.
We can readily tell whether a Eukaryotic cell is ready to divide or has already divided by looking at it under a microscope. Because the nucleus includes genetic material, this is the case. A cell that has chromatin thread in its nucleus is preparing to divide. The presence of chromosomes in the nucleus indicates that the cell has already divided.