What approximate value should come in place of question mark(?) in the following questions?
`(499xx12.02)-:sqrt((443))+1.99^2=?^2`

Options

A. 9
B. 37
C. 17
D. 13

Answer

To solve the equation \( (499 \times 12.02) - \sqrt{443} + 1.99^2 = ?^2 \), we will follow these steps:

### Step 1: Calculate \( 499 \times 12.02 \)
First, we need to multiply 499 by 12.02.

\[ 499 \times 12.02 \approx 6000 \quad (\text{since } 499 \approx 500 \text{ and } 12.02 \approx 12) \]

### Step 2: Calculate \( \sqrt{443} \)
Next, we need to find the square root of 443.

\[ \sqrt{443} \approx 21 \quad (\text{since } 21^2 = 441 \text{ and } 22^2 = 484) \]

### Step 3: Calculate \( 1.99^2 \)
Now, we will calculate \( 1.99^2 \).

\[ 1.99^2 \approx 4 \quad (\text{since } 2^2 = 4) \]

### Step 4: Combine the results
Now we will combine the results from the previous steps:

\[ (499 \times 12.02) - \sqrt{443} + 1.99^2 \approx 6000 - 21 + 4 \]

Calculating this gives:

\[ 6000 - 21 + 4 \approx 6000 - 17 \approx 5983 \]

### Step 5: Set up the equation
We set this equal to \( ?^2 \):

\[ 5983 \approx ?^2 \]

### Step 6: Find the approximate value of \( ? \)
To find \( ? \), we take the square root of 5983:

\[ ? \approx \sqrt{5983} \approx 77.4 \quad (\text{since } 77^2 = 5929 \text{ and } 78^2 = 6084) \]

### Step 7: Check the options
We need to find the closest integer to 77.4 from the options given. The options were 9, 37, 17, and 13. The closest integer is 17.

### Final Answer
Thus, the approximate value that should come in place of the question mark (?) is:

\[ \boxed{17} \]