The value of `(sqrt(0.6912)+sqrt(0.5292))/(sqrt(0.6912)-sqrt(0.5292))` is:

Options

A. 1.5
B. 0.9
C. 15
D. 9

Answer

To solve the expression \((\sqrt{0.6912} + \sqrt{0.5292}) / (\sqrt{0.6912} - \sqrt{0.5292})\), we will follow these steps:

### Step 1: Simplify the Expression
First, we can rewrite the expression as:
\[ \frac{\sqrt{0.6912} + \sqrt{0.5292}}{\sqrt{0.6912} - \sqrt{0.5292}} \]

### Step 2: Eliminate the Decimals
To eliminate the decimals, we can multiply both the numerator and the denominator by \(10000\):
\[ \frac{10000(\sqrt{0.6912} + \sqrt{0.5292})}{10000(\sqrt{0.6912} - \sqrt{0.5292})} \]
This simplifies to:
\[ \frac{\sqrt{6912} + \sqrt{5292}}{\sqrt{6912} - \sqrt{5292}} \]

### Step 3: Calculate the Square Roots
Next, we calculate the square roots:
- \(\sqrt{6912} = \sqrt{576 \times 12} = \sqrt{576} \times \sqrt{12} = 24\sqrt{12}\)
- \(\sqrt{5292} = \sqrt{441 \times 12} = \sqrt{441} \times \sqrt{12} = 21\sqrt{12}\)

Now, substituting these values back into the expression gives us:
\[ \frac{24\sqrt{12} + 21\sqrt{12}}{24\sqrt{12} - 21\sqrt{12}} \]

### Step 4: Factor Out \(\sqrt{12}\)
Factoring out \(\sqrt{12}\) from both the numerator and denominator:
\[ \frac{\sqrt{12}(24 + 21)}{\sqrt{12}(24 - 21)} \]
The \(\sqrt{12}\) cancels out:
\[ \frac{24 + 21}{24 - 21} = \frac{45}{3} \]

### Step 5: Final Calculation
Now, we can simplify:
\[ \frac{45}{3} = 15 \]

Thus, the value of the expression is:
\[ \boxed{15} \]