Basic Technical Mathematics, 11th Edition

Exercises 11.4, page 338

1. 1. $16\sqrt{5}$

2. 3. $8\sqrt{7}$

3. 5. $\sqrt{5}\hspace{0.17em}-\hspace{0.17em}\sqrt{7}$

4. 7. $11\sqrt{2}\hspace{0.17em}-\hspace{0.17em}3\sqrt{3}$

5. 9. $3\sqrt{5}$

6. 11. $\hspace{0.17em}-\hspace{0.17em}4t\sqrt{3}$

7. 13. $\hspace{0.17em}-\hspace{0.17em}3\sqrt{2y}$

8. 15. $19\sqrt{7}$

9. 17. $9\sqrt{2}$

10. 19. $23\sqrt{3R}\hspace{0.17em}-\hspace{0.17em}6\sqrt{2R}$

11. 21. ${\displaystyle \frac{5\sqrt{10}}{2}}$

12. 23. $\hspace{0.17em}-\hspace{0.17em}9\sqrt{2}$

13. 25. $13\sqrt[3]{3}$

14. 27. $\sqrt[4]{2}$

15. 29. $(5a\hspace{0.17em}-\hspace{0.17em}2b^2)\sqrt{ab}$

16. 31. $(3\hspace{0.17em}-\hspace{0.17em}2a)\sqrt{10}$

17. 33. $(2b\hspace{0.17em}-\hspace{0.17em}a)\sqrt[3]{3a^{2}b}$

18. 35. ${\displaystyle \frac{(a^2\hspace{0.17em}-\hspace{0.17em}{c}^3)\sqrt{ac}}{a^2{c}^3}}$

19. 37. ${\displaystyle \frac{(a\hspace{0.17em}-\hspace{0.17em}2b)\sqrt{3a{b}^2}}{ab}}$

20. 39. ${\displaystyle \frac{\hspace{0.17em}-\hspace{0.17em}2V\sqrt{T^2\hspace{0.17em}-\hspace{0.17em}{V}^2}}{T^2\hspace{0.17em}-\hspace{0.17em}{V}^2}}$

21. 41. $8\sqrt{x\hspace{0.17em}+\hspace{0.17em}2}$

22. 43. $15\sqrt{3}\hspace{0.17em}-\hspace{0.17em}11\sqrt{5}\hspace{0.17em}=\hspace{0.17em}1.3840144$

23. 45. ${\displaystyle \frac{1}{6}}\sqrt{6}\hspace{0.17em}=\hspace{0.17em}0.4082483$

24. 47. ${\displaystyle \frac{7}{2}}\sqrt[3]{2}\hspace{0.17em}=\hspace{0.17em}4.4097237$

25. 49. $3\sqrt{3}$

26. 51. Positive, $\sqrt{1000}\hspace{0.17em}=\hspace{0.17em}10\sqrt{10}\hspace{0.17em},\hspace{0.17em}\sqrt{11}\hspace{0.17em}>\hspace{0.17em}\sqrt{10}$

27. 53. $6\sqrt{2}\hspace{0.17em}+\hspace{0.17em}2\sqrt{6}$

28. 55. $18\hspace{0.17em}+\hspace{0.17em}3\sqrt{2}\hspace{0.17em}=\hspace{0.17em}22.2\text{ ft}$