Let's break down the questions in the image and solve them step by step.

A. $\sqrt{28} + 3\sqrt{63} - 2\sqrt{12}$

1. Simplify each square root:

   • $\sqrt{28} = \sqrt{4 \times 7} = 2\sqrt{7}$
   • $\sqrt{63} = \sqrt{9 \times 7} = 3\sqrt{7}$
   • $\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$

2. Substitute the simplified terms: $2\sqrt{7} + 3(3\sqrt{7}) - 2(2\sqrt{3})$ $= 2\sqrt{7} + 9\sqrt{7} - 4\sqrt{3}$

3. Combine like terms: $(2\sqrt{7} + 9\sqrt{7}) - 4\sqrt{3}$ $= 11\sqrt{7} - 4\sqrt{3}$

B. $\sqrt{147} - 2\sqrt{48} + 3\sqrt{12}$

1. Simplify each square root:

   • $\sqrt{147} = \sqrt{49 \times 3} = 7\sqrt{3}$
   • $\sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3}$
   • $\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$

2. Substitute the simplified terms: $7\sqrt{3} - 2(4\sqrt{3}) + 3(2\sqrt{3})$ $= 7\sqrt{3} - 8\sqrt{3} + 6\sqrt{3}$

3. Combine like terms: $(7\sqrt{3} - 8\sqrt{3} + 6\sqrt{3}) = 5\sqrt{3}$

C. $3\sqrt{162} - \sqrt{98} - 2\sqrt{18}$

1. Simplify each square root:

   • $\sqrt{162} = \sqrt{81 \times 2} = 9\sqrt{2}$
   • $\sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}$
   • $\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}$

2. Substitute the simplified terms: $3(9\sqrt{2}) - 7\sqrt{2} - 2(3\sqrt{2})$ $= 27\sqrt{2} - 7\sqrt{2} - 6\sqrt{2}$

3. Combine like terms: $(27\sqrt{2} - 7\sqrt{2} - 6\sqrt{2}) = 14\sqrt{2}$

Final Answers:

• A: $11\sqrt{7} - 4\sqrt{3}$
• B: $5\sqrt{3}$
• C: $14\sqrt{2}$

Would you like more detailed explanations or have any questions?

Here are 5 related questions to practice:

1. Simplify $\sqrt{72} + \sqrt{18} - 3\sqrt{8}$.
2. Solve $4\sqrt{75} - \sqrt{300} + \sqrt{27}$.
3. Simplify $2\sqrt{50} - \sqrt{24} + \sqrt{108}$.
4. Calculate $\sqrt{98} + 2\sqrt{32} - \sqrt{18}$.
5. Simplify $\sqrt{80} - 3\sqrt{20} + \sqrt{45}$.

Tip: Always look for common factors under the square root to simplify complex radicals efficiently.