10 Mid-Chapter Quiz

Do you know HOW?

Use the triangle below. Find the missing side length. If necessary, round to the nearest tenth.

1. a = 20 , b = 25 eh equals 20 comma b equals 25
2. a = 0.8 , b = 1.5 eh equals 0.8 comma b equals 1.5
3. a = 5 , b = 12 eh equals 5 comma b equals 12
4. a = 2.2 , b = 12 eh equals 2.2 comma b equals 12
5. a = 14 , c = 50 eh equals 14 comma c equals 50
6. a = 9 , c = 41 eh equals 9 comma c equals 41
7. b = 40 , c = 41 b equals 40 comma c equals 41
8. b = 36 , c = 39 b equals 36 comma c equals 39

Determine whether the given lengths can be side lengths of a right triangle.

9. 8, 15, 17
10. 5, 24, 25
11. 60, 80, 100

Simplify each radical expression.

12. 80 square root of 80
13. 10 · 18 square root of 10 middle dot square root of 18
14. 6 x · 2 x square root of 6 x end root , middle dot , square root of 2 x end root
15. − 2 3 b 2 · 12 b negative 2 , square root of 3 , b squared end root , middle dot , square root of 12 b end root
16. 64 81 square root of 64 over 81 end root
17. − 5 c 45 c 3 negative . fraction square root of 5 c end root , over square root of 45 , c cubed end root end fraction
18. − 3 14 x 3 − 21 x fraction negative 3 . square root of 14 , x cubed end root , over negative , square root of 21 x end root end fraction
19. 13 f 3 5 f 2 fraction square root of 13 , f cubed end root , over square root of 5 , f squared end root end fraction
20. Sports A rectangular soccer field is 6w yards wide and 10w yards long. What is an expression for the distance from one corner to the opposite corner?

Find the area of each figure.

Simplify each radical expression.

23. 5 5 + 3 5 5 square root of 5 plus 3 square root of 5
24. 2 28 − 3 7 2 square root of 28 minus 3 square root of 7
25. 3 ( 6 − 4 ) square root of 3 . open , square root of 6 minus 4 , close
26. ( 2 21 + 4 3 ) ( 5 21 − 3 ) open . 2 square root of 21 plus 4 square root of 3 . close . open . 5 square root of 21 minus square root of 3 . close
27. 1 3 − 2 fraction 1 , over square root of 3 minus 2 end fraction
28. 3 + 2 4 2 + 2 fraction 3 plus square root of 2 , over 4 square root of 2 plus 2 end fraction

Find the exact solution for each equation. Find the approximate solution to the nearest tenth.

29. 5 8 − 2 = 8 + 2 x fraction 5 , over square root of 8 minus 2 end fraction . equals . fraction square root of 8 plus 2 , over x end fraction
30. x 10 = 3 2 2 + 1 fraction x , over square root of 10 end fraction , equals . fraction 3 square root of 2 , over square root of 2 plus 1 end fraction
31. Transportation A bus leaves the bus station and drives 3.75 mi east. The bus then turns and drives 5 mi south. How far is the bus from the bus station?

Do you UNDERSTAND?

32. What type of angle is formed by the two legs of a right triangle?
33. Writing How do you use a conjugate to simplify a fraction with a radical expression in its denominator?
34. Reasoning Is the equation a + b = a + b square root of eh plus square root of b equals , square root of eh plus b end root  always, sometimes, or never true? Justify your answer.

35. Error Analysis Describe and correct the error shown below in simplifying the radical expression.

    

36. Open-Ended Give the side lengths of a triangle that is not a right triangle. Explain why these lengths cannot be the side lengths of a right triangle.

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