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Let's simplify the given expression step by step:

The expression is:

\[
8\sqrt{3} + \sqrt{12} - \sqrt{75}
\]

### Step 1: Simplify the square roots where possible

- \(\sqrt{12}\) can be written as \(\sqrt{4 \times 3} = 2\sqrt{3}\)
- \(\sqrt{75}\) can be written as \(\sqrt{25 \times 3} = 5\sqrt{3}\)

Now, substitute these simplified terms back into the expression:

\[
8\sqrt{3} + 2\sqrt{3} - 5\sqrt{3}
\]

### Step 2: Combine like terms

Since all terms are multiples of \(\sqrt{3}\), we can combine them:

\[
(8 + 2 - 5)\sqrt{3} = 5\sqrt{3}
\]

### Final Answer:

\[
5\sqrt{3}
\]

Would you like further details on any part of the process?

Here are some follow-up questions for further practice:
1. How would you simplify \(\sqrt{50} + \sqrt{18} - \sqrt{8}\)?
2. Can you simplify \(6\sqrt{2} + 4\sqrt{18} - 3\sqrt{50}\)?
3. What are the steps for simplifying expressions involving square roots?
4. How do you approach combining square roots when their radicands are different?
5. What are some real-life applications of simplifying square root expressions?

**Tip:** Always look for perfect squares within the radicand to simplify square roots easily.

Simplify the expression 8√3 + √12 − √75.

Learn how to simplify the square root expression 8√3 + √12 − √75 by combining like terms and breaking down square roots. This step-by-step guide covers essential concepts in algebra and radical expressions for Grades 8-10.

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