If `sqrt(2)=1.4142`, then find the value of `2xx(sqrt(2))/((2+sqrt(2)))`.

Options

A. `0.8284`
B. `0.8184`
C. `0.8283`
D. `0.8483`

Answer

To solve the expression \( \frac{2 \times \sqrt{2}}{2 + \sqrt{2}} \) given that \( \sqrt{2} = 1.4142 \), we will follow these steps:

### Step 1: Substitute the value of \( \sqrt{2} \)
We start by substituting \( \sqrt{2} \) with its given value:
\[ \frac{2 \times 1.4142}{2 + 1.4142} \]

### Step 2: Calculate the numerator
Now, we calculate the numerator:
\[ 2 \times 1.4142 = 2.8284 \]

### Step 3: Calculate the denominator
Next, we calculate the denominator:
\[ 2 + 1.4142 = 3.4142 \]

### Step 4: Form the fraction
Now we can form the fraction with the calculated numerator and denominator:
\[ \frac{2.8284}{3.4142} \]

### Step 5: Perform the division
Now, we divide the numerator by the denominator:
\[ \frac{2.8284}{3.4142} \approx 0.8284 \]

### Final Answer
Thus, the value of \( \frac{2 \times \sqrt{2}}{2 + \sqrt{2}} \) is approximately:
\[ \boxed{0.8284} \]