Problem 29 Medium Difficulty

(a) Apply Newton's method to the equation $ x^2 - a = 0 $ to derive the following square-root algorithm (used by the ancient Babylonians to compute $ \sqrt{a} $):
$$ x_{n + 1} = \dfrac{1}{2} \left( x_n + \dfrac{a}{x_n} \right) $$

(b) Use part (a) to compute $ \sqrt{1000} $ correct to six decimal places.

Answer

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Video Transcript

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