Let's simplify the expression step by step:

The expression is:

$\sqrt{24} - 2\sqrt{12} + 7\sqrt{6}$

Step 1: Simplify each square root term.

• $\sqrt{24}$ can be written as $\sqrt{4 \times 6} = 2\sqrt{6}$.
• $\sqrt{12}$ can be written as $\sqrt{4 \times 3} = 2\sqrt{3}$.
• $\sqrt{6}$ is already in its simplest form.

Step 2: Substitute the simplified square roots back into the expression.

$2\sqrt{6} - 2(2\sqrt{3}) + 7\sqrt{6}$

This simplifies to:

$2\sqrt{6} - 4\sqrt{3} + 7\sqrt{6}$

Step 3: Combine like terms.

• Combine the $\sqrt{6}$ terms: $2\sqrt{6} + 7\sqrt{6} = 9\sqrt{6}$.

So, the expression becomes:

$9\sqrt{6} - 4\sqrt{3}$

Final answer:

The simplified form of the expression is Option A: $9\sqrt{6} - 4\sqrt{3}$.

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. How can you simplify the square root of any product?
2. What are the steps to combine like terms in a radical expression?
3. How can the distributive property be applied when dealing with square roots?
4. What happens when you have a square root of a perfect square?
5. How do you rationalize a denominator with a square root?

Tip: When simplifying square roots, always look for perfect square factors within the radicand (the number inside the square root).