Practice and Problem-Solving Exercises

A Practice

See Problems 1 and 2.

Simplify each radical expression.

10. 225 square root of 225
11. 99 square root of 99
12. 128 square root of 128
13. − 60 negative square root of 60
14. − 4 117 negative 4 , square root of 117
15. 5 700 5 , square root of 700
16. 192 s 2 square root of 192 , s squared end root
17. 50 t 5 square root of 50 , t to the fifth end root
18. 3 18 a 2 3 . square root of 18 , eh squared end root
19. − 21 27 x 9 negative 21 . square root of 27 , x to the ninth end root
20. 3 150 b 8 3 . square root of 150 , b to the eighth end root
21. − 2 243 y 3 negative 2 . square root of 243 , y cubed end root

See Problem 3.

Simplify each product.

22. 8 · 32 square root of 8 middle dot square root of 32
23. 1 3 6 · 24 1 third , square root of 6 middle dot square root of 24
24. 4 10 · 2 90 4 square root of 10 middle dot 2 square root of 90
25. 5 6 · 1 6 216 5 square root of 6 middle dot , 1 sixth , square root of 216
26. − 5 21 · ( − 3 42 ) negative 5 square root of 21 middle dot . open , negative 3 square root of 42 , close
27. 18 n · 98 n 3 square root of 18 n end root , middle dot . square root of 98 , n cubed end root
28. 3 5 c · 7 15 c 2 3 , square root of 5 c end root , middle dot 7 . square root of 15 , c squared end root
29. 2 y · 128 y 5 square root of 2 y end root , middle dot . square root of 128 , y to the fifth end root
30. − 6 15 s 3 · 2 75 negative 6 . square root of 15 , s cubed end root . middle dot 2 square root of 75
31. − 9 28 a 2 · 1 3 63 a negative 9 . square root of 28 , eh squared end root . middle dot , 1 third . square root of 63 eh end root
32. 10 12 x 3 · 2 6 x 3 10 . square root of 12 , x cubed end root . middle dot 2 , square root of 6 , x cubed end root
33. − 1 3 18 c 5 · ( − 6 8 c 9 ) negative , 1 third . square root of 18 , c to the fifth end root . middle dot . open . negative 6 , square root of 8 , c to the ninth end root . close

See Problem 4.

34. Construction Students are building rectangular wooden frames for the set of a school play. The height of a frame is 6 times the width w. Each frame has a brace that connects two opposite corners of the frame. What is a simplified expression for the length of a brace?
35. Park A park is shaped like a rectangle with a length 5 times its width w. What is a simplified expression for the distance between opposite corners of the park?

See Problems 5 and 6.

Simplify each radical expression.

36. 16 25 square root of 16 over 25 end root
37. 7 6 32 7 , square root of 6 thirty seconds end root
38. − 4 100 729 negative 4 . square root of 100 over 729 end root
39. 3 x 3 64 x 2 square root of fraction 3 , x cubed , over 64 , x squared end fraction end root
40. − 5 162 t 3 2 t negative 5 . square root of fraction 162 , t cubed , over 2 t end fraction end root
41. 11 49 a 5 4 a 3 11 . square root of fraction 49 , eh to the fifth , over 4 , eh cubed end fraction end root
42. 1 11 fraction 1 , over square root of 11 end fraction
43. 5 8 x fraction square root of 5 , over square root of 8 x end root end fraction
44. 3 6 15 fraction 3 square root of 6 , over square root of 15 end fraction
45. 22 11 fraction 22 , over square root of 11 end fraction
46. 2 24 48 t 4 fraction 2 square root of 24 , over square root of 48 , t to the fourth end root end fraction
47. 8 7 s 28 s 3 fraction 8 , square root of 7 s end root , over square root of 28 , s cubed end root end fraction

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