Evaluate `sqrt(16)+sqrt((9.5xx0.0085xx18.9)/(0.021xx0.0017xx1.9))`.

Options

A. 154
B. 158
C. 160
D. 169

Answer

To evaluate the expression \( \sqrt{16} + \sqrt{\frac{9.5 \times 0.0085 \times 18.9}{0.021 \times 0.0017 \times 1.9}} \), we can follow these steps:

### Step 1: Calculate \( \sqrt{16} \)
The square root of 16 is:
\[ \sqrt{16} = 4 \]

### Step 2: Simplify the expression inside the second square root
We need to simplify the expression:
\[ \sqrt{\frac{9.5 \times 0.0085 \times 18.9}{0.021 \times 0.0017 \times 1.9}} \]

### Step 3: Break down the fraction
We can rewrite the fraction as:
\[ \frac{9.5}{0.021} \times \frac{0.0085}{0.0017} \times \frac{18.9}{1.9} \]

### Step 4: Calculate each part of the fraction
1. **Calculate \( \frac{9.5}{0.021} \)**:
\[ \frac{9.5}{0.021} = 452.38 \quad (\text{approximately}) \]

2. **Calculate \( \frac{0.0085}{0.0017} \)**:
\[ \frac{0.0085}{0.0017} = 5 \]

3. **Calculate \( \frac{18.9}{1.9} \)**:
\[ \frac{18.9}{1.9} = 9.947 \quad (\text{approximately}) \]

### Step 5: Combine the results
Now, we can combine these results:
\[ \frac{9.5 \times 0.0085 \times 18.9}{0.021 \times 0.0017 \times 1.9} \approx 452.38 \times 5 \times 9.947 \]

### Step 6: Calculate the product
Calculating the product:
\[ 452.38 \times 5 \approx 2261.9 \]
\[ 2261.9 \times 9.947 \approx 22500 \quad (\text{approximately}) \]

### Step 7: Take the square root
Now we take the square root of the result:
\[ \sqrt{22500} = 150 \]

### Step 8: Combine with the first square root
Now we add the two results together:
\[ 4 + 150 = 154 \]

### Final Answer
Thus, the final answer is:
\[ \boxed{154} \]