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We are asked to find the value of the following expression:

\[
\frac{\sqrt{54}}{\sqrt{12}} + \frac{\sqrt{56}}{\sqrt{63}}
\]

### Step-by-step solution:

1. **Simplifying the first term:**
   \[
   \frac{\sqrt{54}}{\sqrt{12}} = \sqrt{\frac{54}{12}}
   \]
   Simplify \(\frac{54}{12}\):
   \[
   \frac{54}{12} = 4.5 = \frac{9}{2}
   \]
   So:
   \[
   \frac{\sqrt{54}}{\sqrt{12}} = \sqrt{\frac{9}{2}} = \frac{3\sqrt{2}}{2}
   \]

2. **Simplifying the second term:**
   \[
   \frac{\sqrt{56}}{\sqrt{63}} = \sqrt{\frac{56}{63}}
   \]
   Simplify \(\frac{56}{63}\):
   \[
   \frac{56}{63} = \frac{8}{9}
   \]
   So:
   \[
   \frac{\sqrt{56}}{\sqrt{63}} = \sqrt{\frac{8}{9}} = \frac{2\sqrt{2}}{3}
   \]

3. **Adding the two terms:**
   \[
   \frac{3\sqrt{2}}{2} + \frac{2\sqrt{2}}{3}
   \]
   Find the common denominator:
   \[
   \text{LCM of 2 and 3 is 6}
   \]
   Rewrite the terms with the common denominator:
   \[
   \frac{3\sqrt{2}}{2} = \frac{9\sqrt{2}}{6}, \quad \frac{2\sqrt{2}}{3} = \frac{4\sqrt{2}}{6}
   \]
   Now add:
   \[
   \frac{9\sqrt{2}}{6} + \frac{4\sqrt{2}} = \frac{13\sqrt{2}}{6}
   \]

Thus, the value of the expression is \(\frac{13\sqrt{2}}{6}\).

### Answer:
The correct answer is **C**: \(\frac{13\sqrt{2}}{6}\).

---

Do you have any questions, or would you like further details?

Here are 5 related questions to explore:
1. How do you simplify radical expressions involving fractions?
2. Can you explain the process of finding the least common denominator (LCM)?
3. How does simplifying under a square root work when you have a ratio of two numbers?
4. How would the result change if the numbers in the square roots were different?
5. Why do we need to find a common denominator when adding fractions?

**Tip:** Always simplify radicals first before performing any arithmetic operations when dealing with square roots.

Nilai dari √54 / √12 + √56 / √63 adalah ....

This problem involves simplifying radical expressions and adding fractions. We use square root properties and find a common denominator to solve the expression √54 / √12 + √56 / √63, suitable for students in Grades 9-11.

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