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?

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.