Let's go through the problems one by one.

Problem 18:

$-3\sqrt{18} + 3\sqrt{8} - \sqrt{24}$ First, simplify the square roots:

• $\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}$
• $\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}$
• $\sqrt{24} = \sqrt{4 \times 6} = 2\sqrt{6}$

Now substitute them back into the expression: $-3(3\sqrt{2}) + 3(2\sqrt{2}) - 2\sqrt{6}$ Simplify: $-9\sqrt{2} + 6\sqrt{2} - 2\sqrt{6}$ $= -3\sqrt{2} - 2\sqrt{6}$

Problem 20:

$-3\sqrt{5} - \sqrt{6} - \sqrt{5}$ Combine like terms: $(-3\sqrt{5} - \sqrt{5}) - \sqrt{6}$ $= -4\sqrt{5} - \sqrt{6}$

Problem 22:

$-3\sqrt{3} - \sqrt{8} - 3\sqrt{3}$ Simplify $\sqrt{8}$: $\sqrt{8} = 2\sqrt{2}$ Now substitute back: $-3\sqrt{3} - 2\sqrt{2} - 3\sqrt{3}$ Combine like terms: $-6\sqrt{3} - 2\sqrt{2}$

Problem 24:

$2\sqrt{18} - 2\sqrt{12} + 2\sqrt{18}$ Simplify the square roots:

• $\sqrt{18} = 3\sqrt{2}$
• $\sqrt{12} = 2\sqrt{3}$

Substitute them back: $2(3\sqrt{2}) - 2(2\sqrt{3}) + 2(3\sqrt{2})$ Simplify: $6\sqrt{2} - 4\sqrt{3} + 6\sqrt{2}$ Combine like terms: $12\sqrt{2} - 4\sqrt{3}$

Would you like more details or have any questions on these?
Here are 5 related questions for further practice:

1. How do you simplify $\sqrt{32}$?
2. What is the result of $5\sqrt{3} + 7\sqrt{3} - 3\sqrt{3}$?
3. Can you combine $4\sqrt{7} + 3\sqrt{5} - \sqrt{7}$?
4. Simplify $2\sqrt{50} - \sqrt{8} + 3\sqrt{18}$.
5. What is the result of $\sqrt{72} + 4\sqrt{18} - \sqrt{32}$?

Tip: Always look to simplify square roots first before performing operations like addition or subtraction.