Write (T) for true and (F) for false for each of the statements given below:
The square of a prime number is prime.

Answer

To determine whether the statement "The square of a prime number is prime" is true or false, let's analyze it step by step.

### Step 1: Understand what a prime number is.
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. For example, the first few prime numbers are 2, 3, 5, 7, 11, etc.

**Hint:** Remember that a prime number can only be divided evenly by 1 and itself.

### Step 2: Find the square of a prime number.
The square of a number is obtained by multiplying the number by itself. For example:
- The square of 2 (which is prime) is \(2 \times 2 = 4\).
- The square of 3 (which is prime) is \(3 \times 3 = 9\).
- The square of 5 (which is prime) is \(5 \times 5 = 25\).

**Hint:** To find the square of a number, just multiply it by itself.

### Step 3: Check if the squares are prime.
Now, let's check if the squares we calculated are prime:
- 4 is not a prime number (it can be divided by 1, 2, and 4).
- 9 is not a prime number (it can be divided by 1, 3, and 9).
- 25 is not a prime number (it can be divided by 1, 5, and 25).

**Hint:** A number is prime only if it has exactly two distinct positive divisors: 1 and itself.

### Step 4: Conclusion.
Since the squares of the prime numbers we examined (2, 3, and 5) are not prime, we conclude that the statement "The square of a prime number is prime" is false.

**Final Answer:** (F)