A simple method

Calculus Level 1

To find square roots, one can use the following method. Let A A be the number you want to find the square root of. Make an initial guess.

Let your guess be x 0 x_{0} . Then x a + 1 x_{a+1} = 1 / 2 ∗ ( x a + ( A / x a ) ) 1/2 * ( x_{a} + (A/ x_{a}))

Using this method, what is x 2 x_{2} if A = 10 A = 10 and x 0 = 2 x_{0} = 2 ?

89/28 88/29 93/28 187/56

Denton Young by Denton Young , 47, USA

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1 solution

Denton Young
Feb 17, 2016

x 0 x_{0} = 2

x 1 x_{1} = 1/2 (2 + (10/2)) = 7/2

x 2 x_{2} = 1/2 (7/2 + (10/(7/2))) = 1/2 (49/14 + 40/14) = 1/2 (89/14) = 89/28

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Simple standard approach.

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