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標題:

中四maths

發問:

將第1,2題變分數 1) 1.16161616...........16係循環小數 2)-0.122222222........2係偱環小數 rationlize the following 3) (3√2)/√3 4) √2/√8 5) 5/√2 6) (4√10)/√15 evaluate the following 7) (3√27)x(2√12)x√5 8) 4/√6-√6/3 9) (3√5-√3)(2√3+4√5) 10) (√3-√2)(√3+√2) ps:√係開方, /係分數, x係乘

最佳解答:

(1) Let x = 1.1616...., then 100x = 116.1616.... So 100x - x = 115 99x = 115 x = 115/99 (2) Let x = -0.122...., then 10x = -1.222.... So x - 10x = 1.1 -9x = 1.1 x = -1.1/9 = -11/90 (3) (3√2)/√3 = (3√2√3)/3 = √6 (4) √2/√8 = √2/(2√2) = 1/2 (5) 5/√2 = (5√2)/2 (6) (4√10)/√15 = (4√10√15)/15 = (4√150)/15 = (20√6)/15 = (4√6)/3 (7) (3√27) x (2√12) x √5 = (9√3) x (4√3) x √5 = 108√5 (8) 4/√6 - √6/3 = (4√6)/6 - √6/3 = (2√6)/3 - √6/3 = √6/3 (9) (3√5 - √3)(2√3 + 4√5) = 6√15 - 6 + 60 - 4√15 = 54 - 2√15 (10) (√3-√2)(√3+√2) = 3 - 2 = 1

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