Write (T) for true and (F) for false for each of the statements given below:
The sum of two perfect squares is a perfect square.

Answer

To determine whether the statement "The sum of two perfect squares is a perfect square" is true or false, we can analyze it step by step.

### Step 1: Understand Perfect Squares
A perfect square is a number that can be expressed as the square of an integer. For example, the first few perfect squares are:
- \(1^2 = 1\)
- \(2^2 = 4\)
- \(3^2 = 9\)
- \(4^2 = 16\)
- \(5^2 = 25\)

### Step 2: Identify Two Perfect Squares
Let's take two perfect squares as examples:
- The square of 2: \(2^2 = 4\)
- The square of 3: \(3^2 = 9\)

### Step 3: Calculate the Sum of These Perfect Squares
Now, we will add these two perfect squares together:
\[ 4 + 9 = 13 \]

### Step 4: Check if the Sum is a Perfect Square
Next, we need to check if 13 is a perfect square. The perfect squares around 13 are:
- \(3^2 = 9\)
- \(4^2 = 16\)

Since 13 is not equal to \(9\) or \(16\), it is not a perfect square.

### Conclusion
Since we found an example where the sum of two perfect squares (4 and 9) does not result in a perfect square (13), we conclude that the statement "The sum of two perfect squares is a perfect square" is **false**.

### Final Answer
(F)

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