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I see the page contains exercises involving simplifying square roots and other radical expressions. I will go over some problems in more detail:

### 41. Simplify expressions by factoring under the square root:
For example:
- \( \sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2} \)
- \( 3\sqrt{72} = 3 \times \sqrt{36 \times 2} = 18\sqrt{2} \)
- \( \sqrt{80} = \sqrt{16 \times 5} = 4\sqrt{5} \)

### 42. Extract factors from under the square root:
For example:
- \( \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2} \)
- \( \sqrt{24} = \sqrt{4 \times 6} = 2\sqrt{6} \)

### 44. Perform operations and simplify results:
For example:
- \( \sqrt{8} \cdot \sqrt{8} = \sqrt{64} = 8 \)
- \( \sqrt{54} \cdot \frac{6}{4} = \sqrt{54} \cdot \frac{3}{2} = 3\sqrt{6} \)

Would you like more detailed solutions for a specific exercise or additional clarifications on any topic?

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Here are five follow-up questions you might find helpful:
1. How do you simplify \( \sqrt{a \cdot b} \) into its factored form?
2. What happens when you multiply two square roots \( \sqrt{x} \cdot \sqrt{y} \)?
3. How do you simplify \( \sqrt{n^2} \), where \( n \) is an integer?
4. How do you handle negative signs inside a square root, like \( \sqrt{-16} \)?
5. What is the process to rationalize the denominator in an expression like \( \frac{1}{\sqrt{2}} \)?

**Tip:** Always look for perfect square factors inside the square root to simplify expressions easily.

The page contains exercises involving simplifying square roots, extracting factors, and performing operations with radicals.

This guide helps students learn how to simplify and factor radical expressions using square roots and perform operations such as multiplication and division with radicals. It covers key formulas like √(a*b) = √a * √b and steps for solving these expressions. Suitable for Grades 8-10.

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