What is the name of the world's smallest republic, with an area of about 21 square kilometres?

Introduction / Context:
Countries can be classified not only by population and economic power but also by size and form of government. Some of the smallest countries on Earth are tiny island states in the Pacific or microstates in Europe. This question asks you to identify the smallest republic by area, which is a different category from the smallest country overall, because not all small countries are republics.

Given Data / Assumptions:

• The key condition is that the country is a republic.
• The area is about 21 square kilometres.
• Options given are Palermo, Nauru, Vatican City, and Namur.
• We assume basic knowledge of world geography and forms of government.

Concept / Approach:
Nauru is a tiny island nation in the Pacific Ocean and is widely known as the world's smallest republic in terms of land area, at around 21 square kilometres. Vatican City is even smaller in size but is not a republic; it is an ecclesiastical state and an absolute elective monarchy headed by the Pope. Palermo and Namur are not independent countries at all; they are cities in Italy and Belgium respectively. Therefore, the correct answer must be Nauru, which fits both the size and the republican form of government described in the question.

Step-by-Step Solution:
Step 1: Focus on the word republic, which rules out countries that are monarchies or other forms of state. Step 2: Recall that Nauru is a very small independent republic in the Pacific, frequently mentioned in geography as the smallest republic by area. Step 3: Recognise that Vatican City, while smaller, is not a republic but a unique religious monarchy, so it does not meet the condition. Step 4: Note that Palermo and Namur are cities within Italy and Belgium and not independent sovereign states. Step 5: Conclude that Nauru is the only option that correctly matches both the size and the republican government form requirements.

Verification / Alternative check:
Standard geography references and general knowledge books often list Nauru as the smallest republic in the world. In contrast, when discussing the smallest country by area, they mention Vatican City but also note its special status and monarchical government. This differentiation between smallest republic and smallest country supports choosing Nauru for this question.

Why Other Options Are Wrong:
Palermo and Namur are sub national urban areas and not sovereign countries or republics at all. Vatican City is a sovereign microstate but operates as an elective monarchy under the Pope and therefore is not a republic. As a result, none of these options fulfil both criteria given in the question, which are small area and republican form of government.

Common Pitfalls:
A common error is to think of Vatican City whenever a question mentions the smallest country, without paying attention to the qualifier republic. Another pitfall is unfamiliarity with Nauru, which is less often in the news. Carefully reading the wording and remembering that Nauru is the smallest republic by area helps you avoid choosing the more famous but incorrect option of Vatican City.

Final Answer:
The world's smallest republic, with an area of about 21 square kilometres, is Nauru.