The square root of `(9.5 xx 0.085)/(0.017 xx 0.019)` is

Options

A. 0.5
B. 5
C. 50
D. 500

Answer

To solve the expression \(\sqrt{\frac{9.5 \times 0.085}{0.017 \times 0.019}}\), we will simplify it step by step.

### Step 1: Rewrite the numbers in a more manageable form
We can express \(9.5\) and \(0.085\) in terms of fractions:
- \(9.5 = \frac{95}{10}\)
- \(0.085 = \frac{85}{1000} = \frac{85}{10^3}\)

Thus, we can rewrite the expression as:
\[ \sqrt{\frac{\frac{95}{10} \times \frac{85}{10^3}}{0.017 \times 0.019}} \]

### Step 2: Calculate the denominator
Now, we need to calculate the denominator \(0.017 \times 0.019\):
- \(0.017 = \frac{17}{1000}\)
- \(0.019 = \frac{19}{1000}\)

So,
\[ 0.017 \times 0.019 = \frac{17}{1000} \times \frac{19}{1000} = \frac{17 \times 19}{1000 \times 1000} = \frac{323}{10^6} \]

### Step 3: Substitute back into the expression
Now substituting back into our square root expression:
\[ \sqrt{\frac{\frac{95 \times 85}{10 \times 10^3}}{\frac{323}{10^6}}} = \sqrt{\frac{95 \times 85 \times 10^6}{10 \times 10^3 \times 323}} = \sqrt{\frac{95 \times 85 \times 10^6}{10^4 \times 323}} \]

### Step 4: Simplify the expression
Now we can simplify further:
\[ \sqrt{\frac{95 \times 85 \times 10^6}{323 \times 10^4}} = \sqrt{\frac{95 \times 85 \times 10^2}{323}} \]

### Step 5: Calculate \(95 \times 85\)
Calculating \(95 \times 85\):
\[ 95 \times 85 = 8075 \]

### Step 6: Substitute and simplify
Now substituting back:
\[ \sqrt{\frac{8075 \times 10^2}{323}} = \sqrt{\frac{807500}{323}} \]

### Step 7: Calculate the square root
Now we need to calculate \(\sqrt{807500/323}\). First, we can simplify this further:
\[ \sqrt{807500} \approx 284.1 \quad \text{and} \quad \sqrt{323} \approx 17.9 \]
Thus,
\[ \sqrt{\frac{807500}{323}} \approx \frac{284.1}{17.9} \approx 15.9 \]

### Step 8: Final calculation
However, we can also simplify this directly:
\[ \sqrt{25} \cdot 10^{-5} = 5 \cdot 10^{-5} = 0.00005 \]
Thus the final answer is:
\[ \sqrt{25} = 5 \quad \text{and} \quad 10^{-5} = 0.00001 \]

### Conclusion
The final answer is approximately \(50\).

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