What approximate value will come in place of the question mark (?) in the following questions ? (You are not expected to calculate the exact value.)
`?^2+155.98-28.11xx9.16=73.13`

Options

A. 12
B. 26
C. 31
D. 13

Answer

To solve the equation \( ?^2 + 155.98 - 28.11 \times 9.16 = 73.13 \) and find the approximate value of \( ? \), we will follow these steps:

### Step 1: Simplify the equation
Start with the given equation:
\[ ?^2 + 155.98 - 28.11 \times 9.16 = 73.13 \]

### Step 2: Approximate the multiplication
Calculate \( 28.11 \times 9.16 \) approximately. We can round \( 28.11 \) to \( 28 \) and \( 9.16 \) to \( 9 \) for easier calculation:
\[ 28 \times 9 = 252 \]

### Step 3: Substitute the approximate value back into the equation
Now substitute \( 252 \) back into the equation:
\[ ?^2 + 155.98 - 252 = 73.13 \]

### Step 4: Simplify further
Now, simplify the left side:
\[ ?^2 + 155.98 - 252 = 73.13 \]
\[ ?^2 - 96.02 = 73.13 \]

### Step 5: Isolate \( ?^2 \)
Add \( 96.02 \) to both sides:
\[ ?^2 = 73.13 + 96.02 \]
\[ ?^2 \approx 169.15 \]

### Step 6: Take the square root
Now, take the square root of both sides to find \( ? \):
\[ ? \approx \sqrt{169.15} \]

### Step 7: Calculate the approximate value
Since \( \sqrt{169} = 13 \), we can conclude:
\[ ? \approx 13 \]

Thus, the approximate value that will come in place of the question mark (?) is **13**.