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數學知識交流---計算近似值(2)
(1) 不用計算機，不用平方根表， 請列式計算出√29的近似值。 (2) 不用計算機，不用平方根表， 請列式計算出√37的近似值。
最佳解答:
37 = 36 + 1 sqrt(37) = 6 + X with X < 1 => 37 = (6 + X)^2 => 37 = 36 + 12X + X^2 Since X < 1, let X^2 = 0 and we have 12X = 1 and X = 0.083 .083^2 = .007 and this is very small compare to 6 therefore sqrt(37) is about 6.083 and 6.083^2 = 37.003 For sqrt(29), we can use similar technique with sqrt(29) = (5 + X)^2 => 29 = 25 + 10X + X^2 and obtain X = 0.4 However, 0.4^2 = 0.16 and may be a bit too big comparing with 5 One more iteration subsituting X^2 with 0.16, we have 29 = 25 + 10X + 0.16 X = 0.384 In this case, X^2 = 0.147 and 5.384^2 = 28.99
其他解答:
數學知識交流---計算近似值(2)
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發問:(1) 不用計算機，不用平方根表， 請列式計算出√29的近似值。 (2) 不用計算機，不用平方根表， 請列式計算出√37的近似值。
最佳解答:
37 = 36 + 1 sqrt(37) = 6 + X with X < 1 => 37 = (6 + X)^2 => 37 = 36 + 12X + X^2 Since X < 1, let X^2 = 0 and we have 12X = 1 and X = 0.083 .083^2 = .007 and this is very small compare to 6 therefore sqrt(37) is about 6.083 and 6.083^2 = 37.003 For sqrt(29), we can use similar technique with sqrt(29) = (5 + X)^2 => 29 = 25 + 10X + X^2 and obtain X = 0.4 However, 0.4^2 = 0.16 and may be a bit too big comparing with 5 One more iteration subsituting X^2 with 0.16, we have 29 = 25 + 10X + 0.16 X = 0.384 In this case, X^2 = 0.147 and 5.384^2 = 28.99
其他解答:
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