The expression given is:

$8\sqrt{75} - 2\sqrt{12}$

Step 1: Simplify the square roots

• $\sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}$
• $\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$

Step 2: Substitute back into the expression

$8\sqrt{75} - 2\sqrt{12} = 8(5\sqrt{3}) - 2(2\sqrt{3})$ $= 40\sqrt{3} - 4\sqrt{3}$

Step 3: Combine like terms

$40\sqrt{3} - 4\sqrt{3} = 36\sqrt{3}$

Final answer:

$36\sqrt{3}$

Would you like further details or have any other questions?

Here are 5 related questions to expand your understanding:

1. How do you simplify square roots with non-perfect square factors?
2. What is the general rule for factoring out square roots?
3. How can you combine radicals in an expression?
4. What happens if the radicals have different bases? Can they still be combined?
5. How do you rationalize a denominator when simplifying radicals?

Tip: When simplifying square roots, always look for the largest perfect square factor to simplify quickly!