`sqrt((0.00001225)/(0.00005392))` is equal to :

Options

A. `(25)/(77)`
B. `(35)/(73)`
C. `(35)/(77)`
D. `(25)/(73)`

Answer

To solve the expression \( \sqrt{\frac{0.00001225}{0.00005392}} \), we can follow these steps:

### Step 1: Simplify the Fraction
First, we will simplify the fraction inside the square root. We can eliminate the decimals by multiplying both the numerator and the denominator by \( 10^8 \) (to move the decimal point 8 places to the right):

\[ \frac{0.00001225 \times 10^8}{0.00005392 \times 10^8} = \frac{1.225}{5.392} \]

### Step 2: Calculate the Square Root
Now we need to find the square root of the simplified fraction:

\[ \sqrt{\frac{1.225}{5.392}} \]

This can be rewritten as:

\[ \frac{\sqrt{1.225}}{\sqrt{5.392}} \]

### Step 3: Calculate the Square Roots
Next, we will calculate the square roots of the numerator and the denominator separately.

1. **Calculate \( \sqrt{1.225} \)**:
- \( \sqrt{1.225} \approx 1.107 \) (using a calculator or estimation).

2. **Calculate \( \sqrt{5.392} \)**:
- \( \sqrt{5.392} \approx 2.32 \) (using a calculator or estimation).

### Step 4: Divide the Results
Now we can divide the results from the square roots:

\[ \frac{1.107}{2.32} \approx 0.476 \]

### Step 5: Final Result
Thus, the value of \( \sqrt{\frac{0.00001225}{0.00005392}} \) is approximately \( 0.476 \).

### Summary
The final answer is:

\[ \sqrt{\frac{0.00001225}{0.00005392}} \approx 0.476 \]