Write the set {x:x is a positive integer and `x^(2)lt40`} in the Roster Form.

Answer

To write the set {x: x is a positive integer and x² < 40} in roster form, we will follow these steps:

### Step-by-Step Solution:

1. **Understand the Condition**: We need to find positive integers \( x \) such that \( x^2 < 40 \).

2. **Identify Positive Integers**: The positive integers start from 1 and go upwards: 1, 2, 3, 4, 5, 6, 7, ...

3. **Calculate Squares of Positive Integers**:
- \( 1^2 = 1 \)
- \( 2^2 = 4 \)
- \( 3^2 = 9 \)
- \( 4^2 = 16 \)
- \( 5^2 = 25 \)
- \( 6^2 = 36 \)
- \( 7^2 = 49 \) (This exceeds 40)

4. **Determine the Maximum Value of \( x \)**:
- We see that \( 6^2 = 36 \) is less than 40, while \( 7^2 = 49 \) is greater than 40. Therefore, the maximum value of \( x \) that satisfies the condition is 6.

5. **List All Valid Values of \( x \)**:
- The positive integers \( x \) that satisfy \( x^2 < 40 \) are: 1, 2, 3, 4, 5, and 6.

6. **Write in Roster Form**:
- The set in roster form is:
\[ \{1, 2, 3, 4, 5, 6\} \]

### Final Answer:
The set in roster form is \(\{1, 2, 3, 4, 5, 6\}\).