Can a Prime Number be a perfect Square?

Answer: Yes, a prime number can be a perfect square, with 2 being the simplest example (2 x 2 = 4).

Let’s delve into more detail:

1. Prime Numbers Definition:
   • Prime numbers are natural numbers greater than 1 with exactly two distinct positive divisors: 1 and the number itself.
   • Examples include 2, 3, 5, 7, 11, and so on.
2. Perfect Squares Definition:
   • Perfect squares are numbers that result from multiplying an integer by itself.
   • Examples include 1, 4, 9, 16, 25, and so forth.
3. Prime Numbers that are Perfect Squares:
   • The prime number 2 is a perfect square since 2 x 2 equals 4.
   • Other examples include 3 x 3 (9) and 5 x 5 (25).
4. Not All Primes Are Perfect Squares:
   • Primes like 7, 11, 13, and many others are not perfect squares.
   • They cannot be expressed as the product of an integer multiplied by itself.

In summary, while not all prime numbers are perfect squares, there are prime numbers, such as 2, 3, and 5, that are indeed perfect squares. The relationship between primes and perfect squares adds interesting complexity to the study of number theory.