What approximate value should come in place of question mark (?) in the following questions? (You are not expected to calculate the exact value.)
`?^2+142.04-21.97xx7.08=277.03`

Options

A. 5
B. 16
C. 15
D. 17

Answer

To solve the equation \( ?^2 + 142.04 - 21.97 \times 7.08 = 277.03 \), we will follow these steps:

### Step 1: Simplify the equation
Start by simplifying the multiplication in the equation. We need to calculate \( 21.97 \times 7.08 \).

**Approximation**:
- Round \( 21.97 \) to \( 22 \) and \( 7.08 \) to \( 7 \).
- So, \( 22 \times 7 \approx 154 \).

### Step 2: Substitute the approximate value
Now substitute the approximate value back into the equation:

\[ ?^2 + 142 - 154 = 277 \]

### Step 3: Rearrange the equation
Rearranging gives:

\[ ?^2 + 142 - 154 = 277 \]
\[ ?^2 - 12 = 277 \]
\[ ?^2 = 277 + 12 \]
\[ ?^2 = 289 \]

### Step 4: Calculate the square root
Now, take the square root of both sides:

\[ ? = \sqrt{289} \]

### Step 5: Find the approximate value
The square root of \( 289 \) is \( 17 \).

Thus, the approximate value that should come in place of the question mark (?) is **17**.

### Final Answer:
The approximate value is **17**.

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