Solutions to Try Its

1. a. $15$
b. $3$
c. $4$
d. $17$

2. $5|x||y|\sqrt{2yz}$. Notice the absolute value signs around x and y? That’s because their value must be positive!

3. $10|x|$

4. $\frac{x\sqrt{2}}{3{y}^{2}}$. We do not need the absolute value signs for ${y}^{2}$ because that term will always be nonnegative.

5. ${b}^{4}\sqrt{3ab}$

6. $13\sqrt{5}$

7. $0$

8. $6\sqrt{6}$

9. $14 - 7\sqrt{3}$

10. a. $-6$
b. $6$
c. $88\sqrt[3]{9}$

11. ${\left(\sqrt{9}\right)}^{5}={3}^{5}=243$

12. $x{\left(5y\right)}^{\frac{9}{2}}$

13. $28{x}^{\frac{23}{15}}$

Solutions to Odd-Numbered Exercises

1. When there is no index, it is assumed to be 2 or the square root. The expression would only be equal to the radicand if the index were 1.

3. The principal square root is the nonnegative root of the number.

5. 16

7. 10

9. 14

11. $7\sqrt{2}$

13. $\frac{9\sqrt{5}}{5}$

15. 25

17. $\sqrt{2}$

19. $2\sqrt{6}$

21. $5\sqrt{6}$

23. $6\sqrt{35}$

25. $\frac{2}{15}$

27. $\frac{6\sqrt{10}}{19}$

29. $-\frac{1+\sqrt{17}}{2}$

31. $7\sqrt[3]{2}$

33. $15\sqrt{5}$

35. $20{x}^{2}$

37. $7\sqrt{p}$

39. $18{m}^{2}\sqrt{m}$

41. $2b\sqrt{a}$

43. $\frac{15x}{7}$

45. $5{y}^{4}\sqrt{2}$

47. $\frac{4\sqrt{7d}}{7d}$

49. $\frac{2\sqrt{2}+2\sqrt{6x}}{1 - 3x}$

51. $-w\sqrt{2w}$

53. $\frac{3\sqrt{x}-\sqrt{3x}}{2}$

55. $5{n}^{5}\sqrt{5}$

57. $\frac{9\sqrt{m}}{19m}$

59. $\frac{2}{3d}$

61. $\frac{3\sqrt[4]{2{x}^{2}}}{2}$

63. $6z\sqrt[3]{2}$

65. 500 feet

67. $\frac{-5\sqrt{2}-6}{7}$

69. $\frac{\sqrt{mnc}}{{a}^{9}cmn}$

71. $\frac{2\sqrt{2}x+\sqrt{2}}{4}$

73. $\frac{\sqrt{3}}{3}$