`sqrt((0.798)^(2)+0.404xx0.798+(0.202)^(2))+1` is equal to

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
We have:
- \( A = 0.798 \)
- \( B = 0.202 \)
- \( 2AB = 0.404 \)

### Step 2: Rewrite the expression
The expression inside the square root can be rewritten using the formula for the square of a binomial:
\[ A^2 + 2AB + B^2 = (A + B)^2 \]
So we can express:
\[ (0.798)^2 + 0.404 \times 0.798 + (0.202)^2 = (0.798 + 0.202)^2 \]

### Step 3: Calculate \( A + B \)
Now, calculate \( A + B \):
\[ 0.798 + 0.202 = 1 \]

### Step 4: Substitute back into the expression
Now we can substitute back into the square root:
\[ \sqrt{(0.798 + 0.202)^2} + 1 = \sqrt{(1)^2} + 1 \]

### Step 5: Simplify the square root
The square root of \( (1)^2 \) is:
\[ \sqrt{1} = 1 \]

### Step 6: Add 1
Now, add 1 to the result:
\[ 1 + 1 = 2 \]

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