`sqrt((0.798)^(2) + 0.404 xx 0.798 + (0.202)^(2)) + 1 = ?`

Options

A. 0
B. 2
C. 1.596
D. 0.404

Answer

To solve the expression \( \sqrt{(0.798)^2 + 0.404 \times 0.798 + (0.202)^2} + 1 \), we can follow these steps:

### Step 1: Identify the components of the expression
We have:
- \( A = 0.798 \)
- \( B = 0.202 \)
- The term \( 0.404 \) can be rewritten as \( 2 \times 0.202 \times 0.798 \).

### Step 2: Rewrite the expression using the formula for the square of a binomial
We can recognize that the expression inside the square root follows the pattern of the square of a binomial:
\[ A^2 + 2AB + B^2 = (A + B)^2 \]
Thus, we can rewrite:
\[ (0.798)^2 + 0.404 \times 0.798 + (0.202)^2 = (0.798 + 0.202)^2 \]

### Step 3: Calculate \( (0.798 + 0.202) \)
Now, we add the two numbers:
\[ 0.798 + 0.202 = 1.000 \]

### Step 4: Substitute back into the expression
Now, substituting back into the square root:
\[ \sqrt{(0.798 + 0.202)^2} = \sqrt{(1.000)^2} = 1.000 \]

### Step 5: Add 1 to the result
Finally, we add 1 to the result:
\[ 1.000 + 1 = 2 \]

### Final Answer
Thus, the final answer is:
\[ \boxed{2} \]

---