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.