https://file.aiquickdraw.com/mathbot/file/1727268883673cyprt7vq.jpg

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

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### 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:
   \[
   (27\sqrt{2} - 7\sqrt{2} - 6\sqrt{2}) = 14\sqrt{2}
   \]

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### 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.

Calculate the results for the given square root expressions: A. sqrt(28) + 3*sqrt(63) - 2*sqrt(12), B. sqrt(147) - 2*sqrt(48) + 3*sqrt(12), C. 3*sqrt(162) - sqrt(98) - 2*sqrt(18).

Explore how to simplify and solve expressions involving square roots by breaking down complex radicals and combining like terms. This guide provides step-by-step solutions for problems involving operations with square roots, suitable for high school students.

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