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

Options

A. `(5)/(6)`
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 can follow these steps:

### Step 1: Simplify each square root
We can simplify the expression by breaking it down into two parts:
1. \( \sqrt{\frac{0.25}{0.0009}} \)
2. \( \sqrt{\frac{0.09}{0.36}} \)

### Step 2: Simplify \( \sqrt{\frac{0.25}{0.0009}} \)
Convert the decimal values to fractions:
- \( 0.25 = \frac{25}{100} = \frac{1}{4} \)
- \( 0.0009 = \frac{9}{10000} \)

Now, substituting these values into the square root:
\[ \sqrt{\frac{0.25}{0.0009}} = \sqrt{\frac{\frac{1}{4}}{\frac{9}{10000}}} = \sqrt{\frac{1 \times 10000}{4 \times 9}} = \sqrt{\frac{10000}{36}} = \frac{\sqrt{10000}}{\sqrt{36}} = \frac{100}{6} = \frac{50}{3} \]

### Step 3: Simplify \( \sqrt{\frac{0.09}{0.36}} \)
Convert the decimal values to fractions:
- \( 0.09 = \frac{9}{100} \)
- \( 0.36 = \frac{36}{100} = \frac{9}{25} \)

Now, substituting these values into the square root:
\[ \sqrt{\frac{0.09}{0.36}} = \sqrt{\frac{\frac{9}{100}}{\frac{9}{25}}} = \sqrt{\frac{9 \times 25}{9 \times 100}} = \sqrt{\frac{25}{100}} = \frac{\sqrt{25}}{\sqrt{100}} = \frac{5}{10} = \frac{1}{2} \]

### Step 4: Combine the results
Now, we multiply the results from Step 2 and Step 3:
\[ \frac{50}{3} \times \frac{1}{2} = \frac{50 \times 1}{3 \times 2} = \frac{50}{6} = \frac{25}{3} \]

### Final Answer
Thus, the value of the expression \( \sqrt{\frac{0.25}{0.0009}} \times \sqrt{\frac{0.09}{0.36}} \) is \( \frac{25}{3} \).

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