Assertion : `5-sqrt(2)=5-1.414=3.586` is an irrational number .
Reason : The difference of a rational number and an irrational number is an irrational number .

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion .
B. If both assertion and reason are true but reason is not the correct explanation of assertion .
C. If assertion is true but reason is false.
D. If assertion is false but reason is true .

Answer

To solve the problem, we need to analyze the assertion and the reason provided.

**Assertion:** \( 5 - \sqrt{2} = 5 - 1.414 = 3.586 \) is an irrational number.

**Reason:** The difference of a rational number and an irrational number is an irrational number.

### Step-by-Step Solution:

1. **Identify the Components:**
- The number \( 5 \) is a rational number.
- The number \( \sqrt{2} \) is an irrational number.

2. **Calculate the Value of \( 5 - \sqrt{2} \):**
- We know that \( \sqrt{2} \) is approximately \( 1.414 \).
- Therefore, \( 5 - \sqrt{2} \approx 5 - 1.414 = 3.586 \).

3. **Determine the Nature of \( 5 - \sqrt{2} \):**
- Since \( \sqrt{2} \) is irrational, and \( 5 \) is rational, we can apply the rule that states the difference between a rational number and an irrational number is always irrational.
- Thus, \( 5 - \sqrt{2} \) is irrational.

4. **Conclusion:**
- The assertion that \( 5 - \sqrt{2} \) is an irrational number is true.
- The reason provided is also true, as it correctly states that the difference of a rational number and an irrational number is an irrational number.

### Final Statement:
Both the assertion and the reason are true.

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