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The question asks to rationalize the denominator and simplify the expression:

\[
\frac{13}{6\sqrt{10}}
\]

### Step-by-Step Solution:

1. **Rationalize the denominator**:
   To rationalize the denominator, we multiply both the numerator and denominator by \(\sqrt{10}\) so that the square root in the denominator gets eliminated.

   \[
   \frac{13}{6\sqrt{10}} \times \frac{\sqrt{10}}{\sqrt{10}} = \frac{13\sqrt{10}}{6 \times 10} = \frac{13\sqrt{10}}{60}
   \]

2. **Simplification**:
   The fraction \(\frac{13\sqrt{10}}{60}\) cannot be simplified further since 13 and 60 have no common factors. So, the simplified form is:

   \[
   \boxed{\frac{13\sqrt{10}}{60}}
   \]

Would you like more details or further clarifications on any step?

### Related Questions:
1. How do you rationalize a denominator with multiple terms, such as \( \frac{1}{\sqrt{3} + \sqrt{2}} \)?
2. How do you handle rationalizing a denominator with cube roots, like \( \frac{1}{\sqrt[3]{2}} \)?
3. What are the common techniques for simplifying square roots of non-perfect squares?
4. How do you simplify expressions involving higher-order roots like \( \sqrt[4]{16} \)?
5. How do you handle radicals in the numerator, such as \( \frac{\sqrt{5}}{\sqrt{2}} \)?

### Tip:
When rationalizing denominators involving sums or differences of radicals, use the **conjugate** of the denominator to simplify the expression.

Rationalize the denominator and simplify: 13 / (6√10)

Learn how to rationalize the denominator and simplify the expression 13 / (6√10) with a detailed step-by-step solution. This problem covers key algebraic techniques, including rationalizing denominators and simplifying radical expressions. Suitable for students in Grades 9-12.

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