The value of `(4 - sqrt(0.04))/(4 + sqrt(0.4))` is close to

Options

A. 0.4
B. 0.8
C. 1
D. 1.4

Answer

To simplify the expression \((4 - \sqrt{0.04})/(4 + \sqrt{0.4})\), we will follow these steps:

### Step 1: Calculate \(\sqrt{0.04}\)
\[ \sqrt{0.04} = 0.2 \]

### Step 2: Substitute \(\sqrt{0.04}\) into the expression
Now substitute \(0.2\) into the expression:
\[ (4 - 0.2)/(4 + \sqrt{0.4}) \]

### Step 3: Simplify the numerator
\[ 4 - 0.2 = 3.8 \]
So, the expression becomes:
\[ \frac{3.8}{4 + \sqrt{0.4}} \]

### Step 4: Calculate \(\sqrt{0.4}\)
\[ \sqrt{0.4} \approx 0.632 \]

### Step 5: Substitute \(\sqrt{0.4}\) into the expression
Now substitute \(0.632\) into the expression:
\[ 4 + 0.632 = 4.632 \]

### Step 6: Final expression
Now we have:
\[ \frac{3.8}{4.632} \]

### Step 7: Calculate the final value
Now, we can divide:
\[ \frac{3.8}{4.632} \approx 0.82 \]

Thus, the value of \((4 - \sqrt{0.04})/(4 + \sqrt{0.4})\) is close to \(0.82\).

---