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To solve the expression \( 5\sqrt{3} - 5\sqrt{6} + 2\sqrt{3} - \sqrt{6} \), we'll combine like terms.

### Step 1: Combine the terms with \(\sqrt{3}\)
\[
5\sqrt{3} + 2\sqrt{3} = (5 + 2)\sqrt{3} = 7\sqrt{3}
\]

### Step 2: Combine the terms with \(\sqrt{6}\)
\[
-5\sqrt{6} - \sqrt{6} = (-5 - 1)\sqrt{6} = -6\sqrt{6}
\]

### Step 3: Write the final expression
\[
7\sqrt{3} - 6\sqrt{6}
\]

So, the final answer is \( \boxed{7\sqrt{3} - 6\sqrt{6}} \).

Would you like further details or have any questions? Here are five related questions to explore further:

1. How can you simplify an expression with different square roots?
2. What is the geometric interpretation of square roots in expressions?
3. How would this process change if the coefficients were fractions?
4. What are like terms, and why is it important to identify them?
5. How do square roots relate to exponents and their operations?

**Tip:** When simplifying expressions with square roots, always group and combine like terms to simplify the process.

Learn how to simplify the radical expression 5√3 - 5√6 + 2√3 - √6 by combining like terms. This problem covers key algebraic concepts, including radicals and combining like terms. Suitable for students in Grades 8-10.

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