What approximate value will come in place of question mark in the given questions?
`sqrt(100.01)+sqrt(121.09)+sqrt(36.99)-sqrt(?)=(4.99)^2`

Options

A. 20
B. 28
C. 12
D. 4

Answer

To solve the equation \( \sqrt{100.01} + \sqrt{121.09} + \sqrt{36.99} - \sqrt{?} = (4.99)^2 \), we will follow these steps:

### Step 1: Approximate the square roots
1. **Approximate \( \sqrt{100.01} \)**:
- Since \( 100.01 \) is very close to \( 100 \), we can approximate it as:
\[ \sqrt{100.01} \approx \sqrt{100} = 10 \]

2. **Approximate \( \sqrt{121.09} \)**:
- Similarly, \( 121.09 \) is close to \( 121 \), so we approximate:
\[ \sqrt{121.09} \approx \sqrt{121} = 11 \]

3. **Approximate \( \sqrt{36.99} \)**:
- \( 36.99 \) is close to \( 37 \), thus:
\[ \sqrt{36.99} \approx \sqrt{37} \approx 6 \]
(since \( \sqrt{36} = 6 \) and \( \sqrt{37} \) is slightly more than \( 6 \), we can keep it as \( 6 \) for approximation.)

### Step 2: Substitute the approximations into the equation
Now substituting these approximations into the equation:
\[ 10 + 11 + 6 - \sqrt{?} = (4.99)^2 \]

### Step 3: Calculate \( (4.99)^2 \)
- Calculate \( (4.99)^2 \):
\[ (4.99)^2 \approx 25 \quad (\text{since } 5^2 = 25) \]

### Step 4: Set up the equation
Now we have:
\[ 10 + 11 + 6 - \sqrt{?} = 25 \]
Calculating the left side:
\[ 27 - \sqrt{?} = 25 \]

### Step 5: Solve for \( \sqrt{?} \)
Rearranging gives:
\[ -\sqrt{?} = 25 - 27 \]
\[ -\sqrt{?} = -2 \]
Thus,
\[ \sqrt{?} = 2 \]

### Step 6: Square both sides to find \( ? \)
Squaring both sides gives:
\[ ? = 2^2 = 4 \]

### Conclusion
The approximate value that will come in place of the question mark is:
\[ \boxed{4} \]