`(21.98)^(2)-(25.02)^(2)+(13.03)^(2)=?`

Options

A. 25
B. 120
C. 10
D. 65

Explanation

To solve the equation \((21.98)^{2} - (25.02)^{2} + (13.03)^{2}\), we will first round the numbers to the nearest whole numbers and then perform the calculations.

### Step-by-Step Solution:

1. **Rounding the Numbers**:
- Round \(21.98\) to \(22\) (since \(0.98\) is greater than \(0.5\)).
- Round \(25.02\) to \(25\) (since \(0.02\) is less than \(0.5\)).
- Round \(13.03\) to \(13\) (since \(0.03\) is less than \(0.5\)).

So, we rewrite the equation as:
\[ (22)^{2} - (25)^{2} + (13)^{2} \]

2. **Calculating the Squares**:
- Calculate \(22^{2}\):
\[ 22^{2} = 484 \]
- Calculate \(25^{2}\):
\[ 25^{2} = 625 \]
- Calculate \(13^{2}\):
\[ 13^{2} = 169 \]

Now, substitute these values back into the equation:
\[ 484 - 625 + 169 \]

3. **Performing the Operations**:
- First, perform the subtraction:
\[ 484 - 625 = -141 \]
- Then, add \(169\):
\[ -141 + 169 = 28 \]

4. **Final Result**:
The result of the expression is:
\[ 28 \]

However, since we rounded the numbers, we should consider the approximate value. The closest whole number to \(28\) is \(25\).

### Conclusion:
Thus, the final answer is approximately:
\[ \text{Answer} \approx 25 \]