To solve the problem:

Problem: Simplify $3\sqrt{48} + \sqrt{3} - 2\sqrt{75}$

1. Simplify the square roots:

   • $\sqrt{48} = \sqrt{16 \cdot 3} = 4\sqrt{3}$
   • $\sqrt{75} = \sqrt{25 \cdot 3} = 5\sqrt{3}$

2. Rewrite the expression:

   • $3\sqrt{48} + \sqrt{3} - 2\sqrt{75}$
   • $= 3(4\sqrt{3}) + \sqrt{3} - 2(5\sqrt{3})$
   • $= 12\sqrt{3} + \sqrt{3} - 10\sqrt{3}$

3. Combine like terms (all are in $\sqrt{3}$):

   • $12\sqrt{3} + \sqrt{3} - 10\sqrt{3} = (12 + 1 - 10)\sqrt{3} = 3\sqrt{3}$

Final Answer:

B. $3\sqrt{3}$

Would you like a deeper explanation of any step?

Here are five questions to explore further:

1. How do you simplify square roots with factors?
2. Why does $\sqrt{48} = 4\sqrt{3}$?
3. How can we combine terms with the same square root?
4. What happens when there are no like terms in such expressions?
5. Can this process be applied to cubic roots as well?

Tip: Always simplify square roots by factoring out perfect squares!