`sqrt((0.009 xx 0.036 xx 0.016 xx 0.08)/(0.002 xx 0.0008 xx 0.0002))` is equal to

Options

A. 34
B. 36
C. 38
D. 39

Answer

To solve the expression \( \sqrt{\frac{0.009 \times 0.036 \times 0.016 \times 0.08}{0.002 \times 0.0008 \times 0.0002}} \), we will simplify it step by step.

### Step 1: Convert decimals to fractions
We can express the decimals in terms of powers of 10:
- \( 0.009 = 9 \times 10^{-3} \)
- \( 0.036 = 36 \times 10^{-3} = 36 \times 10^{-3} \)
- \( 0.016 = 16 \times 10^{-3} \)
- \( 0.08 = 8 \times 10^{-2} \)
- \( 0.002 = 2 \times 10^{-3} \)
- \( 0.0008 = 8 \times 10^{-4} \)
- \( 0.0002 = 2 \times 10^{-4} \)

### Step 2: Substitute the values into the expression
Now we can substitute these values into the expression:
\[ \sqrt{\frac{(9 \times 10^{-3}) \times (36 \times 10^{-3}) \times (16 \times 10^{-3}) \times (8 \times 10^{-2})}{(2 \times 10^{-3}) \times (8 \times 10^{-4}) \times (2 \times 10^{-4})}} \]

### Step 3: Simplify the numerator
Calculating the numerator:
\[ 9 \times 36 = 324 \]
\[ 324 \times 16 = 5184 \]
\[ 5184 \times 8 = 41472 \]
Now, we also need to account for the powers of 10:
\[ 10^{-3} \times 10^{-3} \times 10^{-3} \times 10^{-2} = 10^{-11} \]
So the numerator becomes:
\[ 41472 \times 10^{-11} \]

### Step 4: Simplify the denominator
Calculating the denominator:
\[ 2 \times 2 = 4 \]
\[ 4 \times 8 = 32 \]
Now, for the powers of 10:
\[ 10^{-3} \times 10^{-4} \times 10^{-4} = 10^{-11} \]
So the denominator becomes:
\[ 32 \times 10^{-11} \]

### Step 5: Combine the results
Now we can combine the numerator and denominator:
\[ \frac{41472 \times 10^{-11}}{32 \times 10^{-11}} = \frac{41472}{32} \]

### Step 6: Perform the division
Calculating \( \frac{41472}{32} \):
\[ 41472 \div 32 = 1296 \]

### Step 7: Take the square root
Now we take the square root:
\[ \sqrt{1296} = 36 \]

### Final Answer
Thus, the final answer is:
\[ \sqrt{\frac{0.009 \times 0.036 \times 0.016 \times 0.08}{0.002 \times 0.0008 \times 0.0002}} = 36 \]