What approximate value will come in place of the question mark (?) in the following questions ?
`(47.23)^2+(27.95)^2-(18.99)^2=?+50.99`

Options

A. 2000
B. 2350
C. 2400
D. 2580

Answer

To solve the equation \( (47.23)^2 + (27.95)^2 - (18.99)^2 = ? + 50.99 \), we will approximate the numbers to make the calculations easier.

### Step 1: Approximate the values
We will round the numbers to the nearest whole numbers:
- \( 47.23 \approx 47 \)
- \( 27.95 \approx 28 \)
- \( 18.99 \approx 19 \)

### Step 2: Write the equation with approximated values
Now we can rewrite the equation using these approximations:
\[ (47)^2 + (28)^2 - (19)^2 = ? + 50.99 \]

### Step 3: Calculate the squares
Now we will calculate the squares of the approximated values:
- \( (47)^2 = 2209 \)
- \( (28)^2 = 784 \)
- \( (19)^2 = 361 \)

### Step 4: Substitute the squares into the equation
Substituting these values back into the equation gives us:
\[ 2209 + 784 - 361 = ? + 50.99 \]

### Step 5: Perform the addition and subtraction
Now we will perform the addition and subtraction on the left side:
\[ 2209 + 784 = 2993 \]
Then,
\[ 2993 - 361 = 2632 \]

### Step 6: Set up the equation to solve for ?
Now we have:
\[ 2632 = ? + 50.99 \]

### Step 7: Isolate the question mark
To find \( ? \), we will subtract \( 50.99 \) from \( 2632 \):
\[ ? = 2632 - 50.99 \]
Calculating this gives:
\[ ? \approx 2632 - 51 = 2581 \]

### Final Answer
The approximate value that will come in place of the question mark (?) is:
\[ ? \approx 2581 \]