B Apply

37. Think About a Plan The design on a parquet floor, shown below, is made of equilateral triangles. The side of a large triangle is 6 in., and the side of a small triangle is 3 in. Find the total area of the design to the nearest tenth of a square inch.

    
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    • How many large and how many small triangles form the design?
    • Can you express the area of an equilateral triangle through its side?

Simplify.

38. 72 + 32 + 18 square root of 72 plus square root of 32 plus square root of 18
39. 75 + 2 48 − 5 3 square root of 75 plus 2 square root of 48 minus 5 square root of 3
40. 5 32 x + 4 98 x 5 , square root of 32 x end root , plus 4 , square root of 98 x end root
41. 75 − 4 18 + 2 32 square root of 75 minus 4 square root of 18 plus 2 square root of 32
42. 4 216 y 2 + 3 54 y 2 4 . square root of 216 , y squared end root . plus 3 . square root of 54 , y squared end root
43. 3 16 3 − 4 54 3 + 128 3 3 , cube root of 16 , , minus 4 , cube root of 54 , , plus , cube root of 128 ,
44. ( 1 + 72 ) ( 5 + 2 ) open , 1 plus square root of 72 , close . open , 5 plus square root of 2 , close
45. ( 3 − 7 ) ( 3 + 2 7 ) open , square root of 3 minus square root of 7 , close . open . square root of 3 plus 2 square root of 7 . close
46. ( y + 2 ) ( y − 7 2 ) open , square root of y plus square root of 2 , close . open . square root of y minus 7 square root of 2 . close
47. ( 12 + 72 ) 2 open . square root of 12 plus square root of 72 . close squared
48. ( 1.25 − 1.8 ) ( 5 + 0.2 ) open . square root of 1.25 , minus , square root of 1.8 . close . open . square root of 5 plus , square root of 0.2 . close
49. ( a + 1 + a − 1 ) ( a + 1 − a − 1 ) open . square root of eh plus 1 end root , plus , square root of eh minus 1 end root . close . open . square root of eh plus 1 end root , minus , square root of eh minus 1 end root . close
50. Error Analysis Describe and correct the error made while simplifying the expression 3 + 2 3 − 2 . fraction 3 plus square root of 2 , over 3 minus square root of 2 end fraction . .

    
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51. Chemistry A scientist found that x grams of Metal A is completely oxidized in 2 x 3 2 x square root of 3  seconds and x grams of Metal B is completely oxidized in 6 x 3 6 x square root of 3  seconds. How much faster is Metal A oxidized than Metal B?
52. Reasoning Describe the possible values of a such that 72 + a square root of 72 plus square root of eh  simplifies to a single term.
53. Writing Discuss the advantages and disadvantages of first simplifying 72 + 32 + 18 square root of 72 plus square root of 32 plus square root of 18  in order to estimate its decimal value.
54. Geometry Show that a right triangle with legs of lengths 2 − 1 square root of 2 minus 1  and 2 + 1 square root of 2 plus 1  is similar to a right triangle with legs of lengths 6 − 32 6 minus square root of 32  and 2.
55. Open-Ended Find two pairs of conjugates with a product of 3.

Rationalize the denominators and simplify.

56. 4 + 27 2 − 3 27 fraction 4 plus square root of 27 , over 2 minus 3 square root of 27 end fraction
57. 4 + 6 2 + 3 fraction 4 plus square root of 6 , over square root of 2 plus square root of 3 end fraction
58. 5 − 21 3 − 7 fraction 5 minus square root of 21 , over square root of 3 minus square root of 7 end fraction
59. 44 x 2 11 + 3 fraction square root of 44 , x squared end root , over square root of 11 plus 3 end fraction
60. 2 + 6 1.5 + 0.5 fraction square root of 2 plus square root of 6 , over square root of 1.5 , plus , square root of 0.5 end fraction
61. 27 − 5 15 − 3 fraction square root of 27 minus square root of 5 , over square root of 15 minus 3 end fraction
62. 4 + 2 3 2 3 fraction 4 plus , cube root of 2 , , over cube root of 2 , end fraction
63. 5 + x 4 x 4 fraction 5 plus , the fourth , root of x , , over the fourth , root of x , end fraction
64. 4 − 2 6 3 4 3 fraction 4 minus 2 , cube root of 6 , , over cube root of 4 , end fraction

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