Consider the following values of the three given numbers `sqrt(103), sqrt(99.35),sqrt(102.20)`
1. 10.1489 (approx)
2. 10.109(approx)
3. 9.967 (approx)
The correct sequence of these values matching with the above numbers is

Options

A. 1,2,3
B. 1,3,2
C. 2,3,1
D. 3,1,2

Answer

To solve the problem, we need to find the approximate values of the square roots of the given numbers and then match them with the provided approximate values.

### Step-by-Step Solution:

1. **Calculate \( \sqrt{103} \)**:
- We know that \( \sqrt{100} = 10 \).
- Since \( 103 \) is slightly greater than \( 100 \), we can estimate \( \sqrt{103} \) to be slightly greater than \( 10 \).
- Using a calculator, we find \( \sqrt{103} \approx 10.1489 \).

2. **Calculate \( \sqrt{99.35} \)**:
- We know that \( \sqrt{100} = 10 \) and \( 99.35 \) is slightly less than \( 100 \).
- Therefore, \( \sqrt{99.35} \) will be slightly less than \( 10 \).
- Using a calculator, we find \( \sqrt{99.35} \approx 9.967 \).

3. **Calculate \( \sqrt{102.20} \)**:
- We know that \( \sqrt{100} = 10 \) and \( 102.20 \) is slightly greater than \( 100 \).
- Therefore, \( \sqrt{102.20} \) will be slightly greater than \( 10 \).
- Using a calculator, we find \( \sqrt{102.20} \approx 10.109 \).

4. **Match the values**:
- Now we have the approximate values:
- \( \sqrt{103} \approx 10.1489 \)
- \( \sqrt{99.35} \approx 9.967 \)
- \( \sqrt{102.20} \approx 10.109 \)
- We can match these values with the given options:
- 1. \( 10.1489 \) matches with \( \sqrt{103} \) (1st)
- 2. \( 10.109 \) matches with \( \sqrt{102.20} \) (3rd)
- 3. \( 9.967 \) matches with \( \sqrt{99.35} \) (2nd)

5. **Determine the correct sequence**:
- The correct sequence of the numbers based on the approximate values is:
- \( \sqrt{103} \) (1st) → \( 10.1489 \)
- \( \sqrt{102.20} \) (3rd) → \( 10.109 \)
- \( \sqrt{99.35} \) (2nd) → \( 9.967 \)
- Thus, the correct sequence is **1, 3, 2**.

### Final Answer:
The correct sequence of these values matching with the above numbers is **1, 3, 2**.