`sqrt((9.5xx0.085)/(0.0017xx0.19))` equals

Options

A. 5
B. 50
C. 500
D. 0.05

Answer

To solve the expression \( \sqrt{\frac{9.5 \times 0.085}{0.0017 \times 0.19}} \), we will follow these steps:

### Step 1: Write the expression clearly
We start with the expression:
\[ \sqrt{\frac{9.5 \times 0.085}{0.0017 \times 0.19}} \]

### Step 2: Convert decimals to fractions
Convert the decimals to fractions for easier calculations:
- \( 9.5 = \frac{95}{10} \)
- \( 0.085 = \frac{85}{1000} \)
- \( 0.0017 = \frac{17}{10000} \)
- \( 0.19 = \frac{19}{100} \)

Substituting these values into the expression gives:
\[ \sqrt{\frac{\frac{95}{10} \times \frac{85}{1000}}{\frac{17}{10000} \times \frac{19}{100}}} \]

### Step 3: Simplify the fractions
Now simplify the fractions:
\[ = \sqrt{\frac{95 \times 85}{10 \times 1000} \div \frac{17 \times 19}{10000}} \]
This can be rewritten as:
\[ = \sqrt{\frac{95 \times 85 \times 10000}{10 \times 1000 \times 17 \times 19}} \]

### Step 4: Simplify the denominator
Calculating the denominator:
\[ 10 \times 1000 = 10000 \]
So we have:
\[ = \sqrt{\frac{95 \times 85 \times 10000}{10000 \times 17 \times 19}} \]
The \(10000\) cancels out:
\[ = \sqrt{\frac{95 \times 85}{17 \times 19}} \]

### Step 5: Calculate the values
Now calculate \( \frac{95}{17} \) and \( \frac{85}{19} \):
- \( 95 \div 17 = 5.588 \) (approximately)
- \( 85 \div 19 = 4.474 \) (approximately)

Now multiply these two results:
\[ = 5.588 \times 4.474 \approx 25 \]

### Step 6: Take the square root
Now take the square root:
\[ \sqrt{25} = 5 \]

### Step 7: Multiply by 10
Finally, since we had \( \sqrt{100} \) in the earlier steps:
\[ 5 \times 10 = 50 \]

### Final Answer
Thus, the value of the expression is:
\[ \boxed{50} \]