Answer Key 9.3

[latexpage]

1. \((2+2+2)\sqrt{5}\)
   \(6\sqrt{5}\)
2. \(-5\sqrt{3}-3\sqrt{6}\)
3. \(-3\sqrt{2}+6\sqrt{5}\)
4. \(-\sqrt{3}-5\sqrt{6}\)
5. \(\sqrt{2}-3\sqrt{9\cdot 2\)
   \(\sqrt{2}-3\cdot 3\sqrt{2}\)
   \(-8\sqrt{2}\)
6. \(-\sqrt{6\cdot 9}-3\sqrt{6}+3\sqrt{9\cdot 3}\)
   \(-3\sqrt{6}-3\sqrt{6}+3\cdot 3\sqrt{3}\)
   \(-6\sqrt{6}+9\sqrt{3}\)
7. \(-3\sqrt{6}-\sqrt{4\cdot 3}+3\sqrt{3}\)
   \(-3\sqrt{6}-2\sqrt{3}+3\sqrt{3}\)
   \(-3\sqrt{6}+\sqrt{3}\)
8. \(-2\sqrt{5}-2\sqrt{6\cdot 9}\)
   \(-2\sqrt{5}-2\cdot 3\sqrt{6}\)
   \(-2\sqrt{5}-6\sqrt{6}\)
9. \(3\sqrt{2}+2\sqrt{4\cdot 2}-3\sqrt{2\cdot 9}\)
   \(3\sqrt{2}+2\cdot 2\sqrt{2}-3\cdot 3\sqrt{2}\)
   \(3\sqrt{2}+4\sqrt{2}-9\sqrt{2}\)
   \(-2\sqrt{2}\)
10. \(4\sqrt{20}-\sqrt{3}\)
    \(4\sqrt{4\cdot 5}-\sqrt{3}\)
    \(4\cdot 2\sqrt{5}-\sqrt{3}\)
    \(8\sqrt{5}-\sqrt{3}\)
11. \(3\sqrt{9\cdot 2}-4\sqrt{2}\)
    \(3\cdot 3\sqrt{2}-4\sqrt{2}\)
    \(9\sqrt{2}-4\sqrt{2}\Rightarrow 5\sqrt{2}\)
12. \(-3\sqrt{9\cdot 3}+2\sqrt{3}-\sqrt{4\cdot 3}\)
    \(-3\cdot 3\sqrt{3}+2\sqrt{3}-2\sqrt{3}\)
    \(-9\sqrt{3}\)
13. \(-3\sqrt{6}-\sqrt{3}\)
14. \(-3\sqrt{2}+3\sqrt{4\cdot 2}+3\sqrt{6}\)
    \(-3\sqrt{2}+3\cdot 2\sqrt{2}+3\sqrt{6}\)
    \(3\sqrt{2}+3\sqrt{6}\)
15. \(-2\sqrt{9\cdot 2}-3\sqrt{4\cdot 2}-\sqrt{4\cdot 5}+2\sqrt{4\cdot 5}\)
    \(-6\sqrt{2}-6\sqrt{2}-2\sqrt{5}+4\sqrt{5}\)
    \(-12\sqrt{2}+2\sqrt{5}\)
16. \(-3\sqrt{9\cdot 2}+3\sqrt{8}\)
    \(-9\sqrt{2}+3\sqrt{4\cdot 2}\)
    \(-9\sqrt{2}+6\sqrt{2}\)
    \(-3\sqrt{2}\)
17. \(-2\sqrt{4\cdot 6}+2\sqrt{5\cdot 4}\)
    \(-4\sqrt{6}+4\sqrt{5}\)
18. \(-3\sqrt{4\cdot 2}-\sqrt{5}-3\sqrt{6}+2\sqrt{9\cdot 2}\)
    \(-6\sqrt{2}-\sqrt{5}-3\sqrt{6}+6\sqrt{2}\)
    \(-\sqrt{5}-3\sqrt{6}\)
19. \(3\sqrt{6\cdot 4}-3\sqrt{3\cdot 9}+2\sqrt{6}+2\sqrt{2\cdot 4}\)
    \(6\sqrt{6}-9\sqrt{3}+2\sqrt{6}+4\sqrt{2}\)
    \(4\sqrt{2}-9\sqrt{3}+8\sqrt{6}\)
20. \(2\sqrt{6}-\sqrt{9\cdot 6}-3\sqrt{9\cdot 3}-\sqrt{3}\)
    \(2\sqrt{6}-3\sqrt{6}-9\sqrt{3}-\sqrt{3}\)
    \(-\sqrt{6}-10\sqrt{3}\)