What approximate value will come in place of question mark (?) in the following questions. (You are not expected to calculate the exact value)
`(23.012 xx 22.989) + 20.985 xx 7.014 = ?^(2)`

Options

A. 8
B. 38
C. 26
D. 12

Answer

To solve the problem, we need to approximate the values in the expression and find the value of \( ? \) such that:

\[ (23.012 \times 22.989) + (20.985 \times 7.014) = ?^2 \]

### Step 1: Approximate the first multiplication
We start with the first term, \( 23.012 \times 22.989 \).

**Approximation:**
- Round \( 23.012 \) to \( 23 \).
- Round \( 22.989 \) to \( 23 \).

So, we can approximate:
\[ 23.012 \times 22.989 \approx 23 \times 23 = 529 \]

**Hint:** When approximating, round the numbers to the nearest whole number for easier multiplication.

### Step 2: Approximate the second multiplication
Next, we approximate the second term, \( 20.985 \times 7.014 \).

**Approximation:**
- Round \( 20.985 \) to \( 21 \).
- Round \( 7.014 \) to \( 7 \).

So, we can approximate:
\[ 20.985 \times 7.014 \approx 21 \times 7 = 147 \]

**Hint:** Again, round the numbers to the nearest whole number to simplify calculations.

### Step 3: Add the two approximated results
Now, we add the results from Step 1 and Step 2:
\[ 529 + 147 = 676 \]

**Hint:** Make sure to add the approximated results carefully to avoid errors.

### Step 4: Find the square root
We need to find \( ? \) such that:
\[ ?^2 = 676 \]

To find \( ? \), we take the square root of \( 676 \):
\[ ? = \sqrt{676} = 26 \]

**Hint:** Remember that the square root of a number gives you the original number when squared.

### Conclusion
Thus, the approximate value that will come in place of the question mark (?) is:
\[ \boxed{26} \]