`sqrt( (0.25)/(0.0009) ) xx sqrt( (0.09)/(0.36))` is equal to

Options

A. `5/9`
B. `7 (1)/(6)`
C. `7 (1)/(3)`
D. `8 (1)/(3)`

Answer

To solve the expression \( \sqrt{\frac{0.25}{0.0009}} \times \sqrt{\frac{0.09}{0.36}} \), we will follow these steps:

### Step 1: Convert decimals to fractions
We start by converting the decimals to fractions:
- \( 0.25 = \frac{25}{100} \)
- \( 0.0009 = \frac{9}{10000} \)
- \( 0.09 = \frac{9}{100} \)
- \( 0.36 = \frac{36}{100} \)

### Step 2: Rewrite the expression
Now we can rewrite the expression using these fractions:
\[ \sqrt{\frac{\frac{25}{100}}{\frac{9}{10000}}} \times \sqrt{\frac{\frac{9}{100}}{\frac{36}{100}}} \]

### Step 3: Simplify the fractions
We simplify the fractions inside the square roots:
1. For the first term:
\[ \frac{\frac{25}{100}}{\frac{9}{10000}} = \frac{25 \times 10000}{100 \times 9} = \frac{250000}{900} = \frac{2500}{9} \]
2. For the second term:
\[ \frac{\frac{9}{100}}{\frac{36}{100}} = \frac{9}{36} = \frac{1}{4} \]

### Step 4: Substitute back into the expression
Now we substitute back into the expression:
\[ \sqrt{\frac{2500}{9}} \times \sqrt{\frac{1}{4}} \]

### Step 5: Combine the square roots
Using the property of square roots, we can combine them:
\[ \sqrt{\frac{2500 \times 1}{9 \times 4}} = \sqrt{\frac{2500}{36}} \]

### Step 6: Simplify the square root
Now we simplify the square root:
\[ \sqrt{\frac{2500}{36}} = \frac{\sqrt{2500}}{\sqrt{36}} = \frac{50}{6} \]

### Step 7: Simplify the fraction
Now we simplify \( \frac{50}{6} \):
\[ \frac{50}{6} = \frac{25}{3} \]

### Step 8: Convert to mixed fraction
To convert \( \frac{25}{3} \) to a mixed fraction:
- \( 25 \div 3 = 8 \) remainder \( 1 \)
- Thus, \( \frac{25}{3} = 8 \frac{1}{3} \)

### Final Answer
The final answer is:
\[ 8 \frac{1}{3} \]