Practice and Problem-Solving Exercises

A Practice

A See Problem 1.

Simplify each expression.

9. 36 square root of 36
10. 169 square root of 169
11. 16 square root of 16
12. 900 square root of 900
13. 36 49 square root of 36 over 49 end root
14. 25 81 square root of 25 over 81 end root
15. 1 9 square root of 1 ninth end root
16. 121 16 square root of 121 over 16 end root
17. 1.96 square root of 1.96
18. 0.25 square root of 0.25

See Problem 2.

Estimate the square root. Round to the nearest integer.

19. 17 square root of 17
20. 35 square root of 35
21. 242 square root of 242
22. 61 square root of 61
23. 320 square root of 320

Find the approximate side length of each square figure to the nearest whole unit.

24. a mural with an area of 18 m 2 18 , m squared
25. a game board with an area of 160 in. 2 160 , in. squared
26. a helicopter launching pad with an area of 3000 ft 2 3000 , ft squared

See Problem 3.

Name the subset(s) of the real numbers to which each number belongs

27. 2 3 2 thirds
28. 13
29. − 1 negative 1
30. − 19 100 negative , 19 over 100
31. π
32. − 2.38 negative , 2.38
33. 17 4573 17 over 4573
34. 144 square root of 144
35. 113 square root of 113
36. 59 2 59 over 2

See Problem 4.

Compare the numbers in each exercise using an inequality symbol.

37. 5 2 3 , 5 , and 2 thirds , comma 29 square root of 29
38. − 3.1 , − 16 5 negative 3.1 comma , negative , 16 over 5
39. 4 3 2 4 thirds , square root of 2
40. 9.6, 96 square root of 96
41. − 7 11 , − 0.63 negative , 7 elevenths , comma . minus , 0.63
42. 115 , square root of 115 , comma  10.72104 …
43. − 22 25 , − 0. 8 ¯ negative , 22 over 25 , comma negative 0. , 8 bar
44. 184 , square root of 184 , comma  15.56987 …

See Problem 5.

Order the numbers in each exercise from least to greatest.

45. 1 2 , − 2 , 5 , − 7 4 , 1 half , comma , minus 2 comma , square root of 5 comma . negative , 7 fourths , comma  2.4
46. − 3 , 31 , 11 , 5.5 , − 60 11 negative 3 comma square root of 31 comma square root of 11 comma 5.5 comma negative , 60 over 11
47. − 6 , 20 , 4.3 , − 59 9 negative 6 comma square root of 20 comma 4.3 comma negative , 59 over 9
48. 10 3 , 10 over 3 , comma  3, 8 , square root of 8 comma  2.9, 7 square root of 7
49. − 13 6 , − 2.1 , − 26 13 , − 9 4 negative , 13 over 6 , comma negative 2.1 comma negative , 26 over 13 , comma negative , 9 fourths
50. − 1 6 , − 0.3 , 1 , − 2 13 , 7 8 negative , 1 sixth , comma negative 0.3 comma square root of 1 comma negative , 2 thirteenths , comma , 7 eighths

Table of Contents