https://file.aiquickdraw.com/mathbot/file/1729248577360ybn1lze9.jpg

The problem asks to simplify the expression:

\[
\frac{\sqrt{27} - \sqrt{24}}{\sqrt{3}}
\]

### Step 1: Simplify the square roots
- \(\sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}\)
- \(\sqrt{24} = \sqrt{4 \times 6} = 2\sqrt{6}\)

So the expression becomes:

\[
\frac{3\sqrt{3} - 2\sqrt{6}}{\sqrt{3}}
\]

### Step 2: Split the terms
We can rewrite the expression as two separate terms:

\[
\frac{3\sqrt{3}}{\sqrt{3}} - \frac{2\sqrt{6}}{\sqrt{3}}
\]

### Step 3: Simplify each term
1. For the first term:

\[
\frac{3\sqrt{3}}{\sqrt{3}} = 3
\]

2. For the second term, use the property \(\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}\):

\[
\frac{2\sqrt{6}}{\sqrt{3}} = 2\sqrt{\frac{6}{3}} = 2\sqrt{2}
\]

### Step 4: Final expression
Now the expression simplifies to:

\[
3 - 2\sqrt{2}
\]

### Conclusion
This matches answer **B. \(-2\sqrt{2} + 3\)**, which is the correct choice.

Would you like more details or have any questions?

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Here are some related questions:
1. How do you simplify radicals like \(\sqrt{27}\) or \(\sqrt{24}\)?
2. Why does \(\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}\) work?
3. What other strategies are there for simplifying expressions with square roots?
4. Can this process be applied to complex numbers?
5. How does the distributive property relate to simplifying square roots?

**Tip:** Always look for perfect squares inside the radical to simplify expressions!

Which of the following is equivalent to (√27 - √24) / √3?

Learn how to simplify the radical expression (√27 - √24) / √3 step by step. The problem covers simplifying square roots and radicals, perfect squares, and using key radical properties. Ideal for students in Grades 9-10.

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