What will come in place of the question mark (?) in the following questions ?
`(23.1)^(2) + (48.6)^(2) - (39.8)^(2) = ? + 1147.69`

Options

A. A) `(13.6)^(2)`
B. B) `sqrt(12.8)`
C. C) `163.84`
D. D) `12.8`

Answer

To solve the equation \( (23.1)^{2} + (48.6)^{2} - (39.8)^{2} = ? + 1147.69 \), we will follow these steps:

### Step 1: Calculate \( (23.1)^{2} \)
\[ (23.1)^{2} = 23.1 \times 23.1 = 533.61 \]

**Hint:** To square a number, multiply it by itself.

### Step 2: Calculate \( (48.6)^{2} \)
\[ (48.6)^{2} = 48.6 \times 48.6 = 2361.96 \]

**Hint:** Use the same method of multiplying the number by itself to find the square.

### Step 3: Calculate \( (39.8)^{2} \)
\[ (39.8)^{2} = 39.8 \times 39.8 = 1584.04 \]

**Hint:** Again, multiply the number by itself to find the square.

### Step 4: Substitute the calculated values into the equation
Now substitute the calculated squares into the equation:
\[ 533.61 + 2361.96 - 1584.04 = ? + 1147.69 \]

### Step 5: Perform the addition and subtraction
First, add \( 533.61 \) and \( 2361.96 \):
\[ 533.61 + 2361.96 = 2895.57 \]
Then subtract \( 1584.04 \):
\[ 2895.57 - 1584.04 = 1311.53 \]

### Step 6: Set up the equation to solve for ?
Now we have:
\[ 1311.53 = ? + 1147.69 \]

### Step 7: Isolate the question mark
To find \( ? \), subtract \( 1147.69 \) from \( 1311.53 \):
\[ ? = 1311.53 - 1147.69 = 163.84 \]

### Final Answer
Thus, the value that comes in place of the question mark (?) is:
\[ \boxed{163.84} \]