The given mathematical problem is:

$2\sqrt{75} + \sqrt{48} - 4\sqrt{27}$

Step 1: Simplify each square root term

1. $\sqrt{75} = \sqrt{25 \cdot 3} = 5\sqrt{3}$ Therefore, $2\sqrt{75} = 2 \cdot 5\sqrt{3} = 10\sqrt{3}$.

2. $\sqrt{48} = \sqrt{16 \cdot 3} = 4\sqrt{3}$.

3. $\sqrt{27} = \sqrt{9 \cdot 3} = 3\sqrt{3}$, so $4\sqrt{27} = 4 \cdot 3\sqrt{3} = 12\sqrt{3}$.

Step 2: Combine terms

Now substitute the simplified terms into the expression:

$2\sqrt{75} + \sqrt{48} - 4\sqrt{27} = 10\sqrt{3} + 4\sqrt{3} - 12\sqrt{3}$

Combine the coefficients of $\sqrt{3}$:

$(10 + 4 - 12)\sqrt{3} = 2\sqrt{3}$

Final Answer:

$\boxed{2\sqrt{3}}$

Would you like additional explanation or assistance with similar problems? Here are some related questions to expand your understanding:

1. How do you simplify other square root expressions like $\sqrt{200}$ or $\sqrt{32}$?
2. What are the rules for combining like terms in radical expressions?
3. Can you provide the geometric interpretation of $\sqrt{75}$ or similar roots?
4. How does rationalizing denominators relate to simplifying square roots?
5. Can you solve an expression where radicals involve variables, e.g., $\sqrt{4x^2} + \sqrt{16x^4}$?

Tip: Always break down radicals into their prime factors for easy simplification.