Let's simplify the expression:

\[
\sqrt{6} - 2\sqrt{24} + 3\sqrt{96}
\]

### Step 1: Simplify each square root
- \(\sqrt{6}\) stays as it is (it cannot be simplified further).
- \(\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6}\).
- \(\sqrt{96} = \sqrt{16 \times 6} = \sqrt{16} \times \sqrt{6} = 4\sqrt{6}\).

### Step 2: Substitute the simplified square roots back into the expression:
\[
\sqrt{6} - 2(2\sqrt{6}) + 3(4\sqrt{6})
\]

### Step 3: Multiply and combine like terms:
- \(2(2\sqrt{6}) = 4\sqrt{6}\),
- \(3(4\sqrt{6}) = 12\sqrt{6}\).

Now, substitute these into the expression:
\[
\sqrt{6} - 4\sqrt{6} + 12\sqrt{6}
\]

### Step 4: Combine like terms:
\[
(\sqrt{6} - 4\sqrt{6} + 12\sqrt{6}) = (1\sqrt{6} - 4\sqrt{6} + 12\sqrt{6}) = 9\sqrt{6}
\]

### Final answer:
\[
9\sqrt{6}
\]

Would you like further details or have any questions?

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Here are 5 related questions to explore further:
1. How do you simplify square roots with different numbers inside?
2. Can you explain how to combine like terms with square roots?
3. What is the difference between simplifying a square root and factoring it?
4. How do square roots behave with multiplication and division?
5. How can we simplify more complex radical expressions?

**Tip:** Always check if the number inside a square root can be factored into a perfect square to simplify the expression.

Learn how to simplify the expression \sqrt{6}-2\sqrt{24}+3\sqrt{96} by applying properties of square roots and combining like terms. This problem helps students practice simplifying radical expressions. Suitable for students in Grades 8-10.

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