Assertion : If `sqrt(2)=1.414, sqrt(3)=1.732` , then `sqrt(5)=sqrt(2)+sqrt(3)` .
Reason : Square root of a positive real number always exists .

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 assertion and reason given in the question, we need to analyze both statements separately.

### Step 1: Evaluate the Assertion
The assertion states that \( \sqrt{5} = \sqrt{2} + \sqrt{3} \).

1. We know the approximate values:
- \( \sqrt{2} \approx 1.414 \)
- \( \sqrt{3} \approx 1.732 \)

2. Now, let's calculate \( \sqrt{2} + \sqrt{3} \):
\[ \sqrt{2} + \sqrt{3} \approx 1.414 + 1.732 = 3.146 \]

3. Next, we need to find the approximate value of \( \sqrt{5} \):
- The approximate value of \( \sqrt{5} \) is \( 2.236 \).

4. Compare the two results:
\[ \sqrt{5} \approx 2.236 \quad \text{and} \quad \sqrt{2} + \sqrt{3} \approx 3.146 \]

5. Since \( 2.236 \neq 3.146 \), the assertion is **false**.

### Step 2: Evaluate the Reason
The reason states that the square root of a positive real number always exists.

1. This is a true statement. For any positive real number \( x \), \( \sqrt{x} \) is defined and exists in the real number system.

### Conclusion
- The assertion is **false**.
- The reason is **true**.

### Final Answer
The assertion is false, while the reason is true.

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