To combine the radicals \(\sqrt{6x} + 5\sqrt{6x} - \frac{8}{6x}\), follow these steps:

1. **Combine Like Terms:**
   - The terms \(\sqrt{6x}\) and \(5\sqrt{6x}\) are like terms, meaning they can be combined.
   \[
   \sqrt{6x} + 5\sqrt{6x} = 6\sqrt{6x}
   \]

2. **Simplify the Expression:**
   - Now, substitute the combined terms back into the expression:
   \[
   6\sqrt{6x} - \frac{8}{6x}
   \]
   - This is the simplified form of the expression.

Thus, the simplified expression is:

\[
6\sqrt{6x} - \frac{8}{6x}
\]

Let me know if you need further details or have any questions.

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Here are 8 related questions to further explore this topic:

1. How do you simplify expressions with different radicals?
2. What are like terms, and how do you identify them in an expression?
3. How would you combine the radicals \( \sqrt{3x} + 2\sqrt{3x} \)?
4. Can you combine \( \sqrt{6x} \) with \( \sqrt{12x} \)? Why or why not?
5. How do you rationalize the denominator in an expression like \( \frac{1}{\sqrt{6x}} \)?
6. What is the process for adding radicals with different coefficients?
7. How would you simplify an expression with multiple different radicals?
8. How can you simplify a radical expression involving variables and coefficients?

**Tip:** When combining radicals, always ensure the radicands (the expressions under the radicals) are the same; only then can they be combined like regular algebraic terms.

Learn how to combine radicals and simplify the expression √6x + 5√6x - 8/6x step-by-step. This problem involves understanding radicals and combining like terms in algebra. Suitable for Grades 9-12.

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