Practice and Problem-Solving Exercises

A Practice

See Problems 1 and 2.

Simplify each sum or difference.

9. 5 + 6 5 square root of 5 plus 6 square root of 5
10. 12 5 − 3 5 12 square root of 5 minus 3 square root of 5
11. 7 3 + 3 7 square root of 3 plus square root of 3
12. 4 2 − 7 2 4 square root of 2 minus 7 square root of 2
13. 3 7 − 63 3 square root of 7 minus square root of 63
14. 4 128 + 5 18 4 , square root of 128 , plus 5 square root of 18
15. 3 45 − 8 20 3 square root of 45 minus 8 square root of 20
16. 28 − 5 7 square root of 28 minus 5 square root of 7
17. − 6 10 + 5 90 negative 6 square root of 10 plus 5 square root of 90
18. 3 3 − 2 12 3 square root of 3 minus 2 square root of 12
19. − 1 2 5 + 2 125 negative , 1 half , square root of 5 plus 2 , square root of 125
20. 5 8 + 2 72 5 square root of 8 plus 2 square root of 72

See Problem 3.

Simplify each product.

21. 6 ( 2 + 3 ) square root of 6 . open , square root of 2 plus square root of 3 , close
22. 5 ( 15 − 3 ) square root of 5 . open , square root of 15 minus 3 , close
23. 3 7 ( 1 − 7 ) 3 square root of 7 . open , 1 minus square root of 7 , close
24. − 12 ( 4 − 2 3 ) negative square root of 12 . open . 4 minus 2 square root of 3 . close
25. 5 11 ( 3 − 3 2 ) 5 square root of 11 . open . square root of 3 minus 3 square root of 2 . close
26. ( 3 11 + 7 ) 2 open . 3 square root of 11 plus square root of 7 . close squared
27. ( 2 + 10 ) ( 2 − 10 ) open , 2 plus square root of 10 , close . open , 2 minus square root of 10 , close
28. ( 6 + 3 ) ( 2 − 2 ) open , square root of 6 plus square root of 3 , close . open , square root of 2 minus 2 , close
29. ( 5 2 − 2 3 ) 2 open . 5 square root of 2 minus 2 square root of 3 . close squared

See Problem 4.

Simplify each quotient.

30. 5 2 − 1 fraction 5 , over square root of 2 minus 1 end fraction
31. 3 7 − 3 fraction 3 , over square root of 7 minus square root of 3 end fraction
32. − 2 6 + 11 fraction negative 2 , over square root of 6 plus square root of 11 end fraction
33. 5 2 − 5 fraction square root of 5 , over 2 minus square root of 5 end fraction
34. − 1 2 − 2 3 fraction negative 1 , over 2 minus 2 square root of 3 end fraction
35. 7 5 + 13 fraction 7 , over square root of 5 plus square root of 13 end fraction

See Problem 5.

36. Biology A shell fits into a golden rectangle with a length of 8 in. What is the shell's width? Write your answer in simplified radical form and rounded to the nearest tenth of an inch.
37. Architecture A room is approximately shaped like a golden rectangle. Its length is 23 ft. What is the room's width? Write your answer in simplified radical form and rounded to the nearest tenth of a foot.

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