1. Simplify √ 196. If no answer exists, state “not real.” 14

2. Simplify – √ – 36. If no answer exists, state “not real.” not real

3. Simplify √ – 25. If no answer exists, state “not real.” not real

4. Simplify – √16. If no answer exists, state “not real.” – 4– 4– 4– 4

5. Simplify √ 25 + 144. 13

6. Simplify. 4 √ 121 √ 36 22 3

7. Simplify 2 √ 25 – 16 + √ 81. 15

8. Simplify √ 36(4). 12

9. Find the consecutive integers between which √ 11 lies. 3 and 4

10. Find the consecutive integers between which – √ 147 lies. – 13 and – 12

11. Find the consecutive integers between which √ 36 lies. 3 and 4 33

12. Find the consecutive integers between which √ – 70 lies. 33 – 5 and – 4

13. Estimate √ 21 to the nearest tenth. 4.6

14. Estimate √ 116 to the nearest tenth. 10.8

15. Solve √ x – 5 = – 2. If no answer exists, state “no real solution.” x = 9

16. Solve √ x = 1.7. If no answer exists, state “no real solution.” x = 2.89

17. Solve 3 √ 2x + 9 = 0. If no answer exists, state “no real solution.” no real solution

18. Solve 2 √ 4x – 3 = 6. If no answer exists, state “no real solution.” x = 3

19. Solve. Leave answers in simplified radical form if the radicand is not a perfect square. If no answer exists, state “no real solution.” Solve x 2 + 31 = 112. x = ± 9

20. Solve 7x 2 = 56. x = ± 2 √ 2

21. Solve x 2 /3 – 1 = 11 x = ± 6

22. Solve 4x 2 + 12 = 8. no real solution

23. If the lengths of the legs of a right triangle are 15 and 8, find the hypotenuse. Simplify irrational roots or round to the nearest tenth. 17

24. If the lengths of the legs of a right triangle are 5 and 5, find the hypotenuse. Simplify irrational roots or round to the nearest tenth. 5 √ 2 ≈ 7.1

25. Given a hypotenuse of 34 and one leg of 30, find the missing leg. Simplify irrational roots or round to the nearest tenth. 16

26. Given a hypotenuse of 6 and one leg of 3, find the missing leg. Simplify irrational roots or round to the nearest tenth. 3 √ 3 ≈ 5.2

27. Given three side lengths of 10, 25, and 27, determine whether the triangle is a right triangle. no

28. Given three side lengths of 16, 30, and 34, determine whether the triangle is a right triangle. yes

29. Simplify √ 8,100. 90

30. Simplify √ 250,000. 500

31. Simplify √ 252. 6 √ 76 √ 76 √ 76 √ 7

32. Simplify √ 80. 4 √ 54 √ 54 √ 54 √ 5

33. Simplify √ 6 √ 30. 6 √ 56 √ 56 √ 56 √ 5

34. Simplify 3 √ 10 (2 √ 15). 30 √ 6

35. Simplify. √ 36 √ 2 3 √ 23 √ 23 √ 23 √ 2

36. Simplify. 25 121 5 11

37. Simplify. 3√ 8 6 √ 2 √ 2 √ 2 √ 2

38. Simplify 7 √ 3 – 3 √ 3 + √ 3. 5 √ 35 √ 35 √ 35 √ 3

39. Simplify 9 √ 5 + √ 5 – 6 √ 7. 10 √ 5 – 6 √ 7

40. Simplify 2 √ 50 – √ 72. 4 √ 24 √ 24 √ 24 √ 2

41. Simplify 3 √ 27 – √ 125 + 2 √ 75 + √ 45. 19 √ 3 – 2 √ 5

42. Find (– 4) 3. – 64

43. Find 5 3. 125

44. Find √ – 1. 33 – 1– 1– 1– 1

45. Find √ 216. 33 66

46. Find √ 1,331. 33 11

47. Give the mathematical significance of Revelation 21:16.