Let's simplify the expression step by step:

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

Step 1: Simplify each square root.

1. $\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}$
2. $\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3}$
3. $\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}$

Step 2: Substitute the simplified values back into the expression.

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

This becomes:

$4\sqrt{3} + 5\sqrt{3} - 2\sqrt{2}$

Step 3: Combine like terms.

$(4\sqrt{3} + 5\sqrt{3}) - 2\sqrt{2} = 9\sqrt{3} - 2\sqrt{2}$

Final Answer:

$9\sqrt{3} - 2\sqrt{2}$

Would you like more details on the simplification process or have any further questions?

Related questions:

1. How do you simplify square roots with other composite numbers?
2. What are the properties of square roots that allow for factoring?
3. How do you perform operations with square roots involving different radicands?
4. Can you solve an equation involving square roots?
5. What is the difference between simplifying square roots and rationalizing them?

Tip: When simplifying square roots, always look for perfect squares that can be factored out to make the expression simpler.