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Use Newton's Method to approximate the fifth root of twenty to eight decimal places.
Set the function equal to x, and then simplify. Move all terms to one side, setting the function
equal to zero. Then set the function equal to f of x. Take the derivative to get f prime
of x. Choose a rough estimate for the fifth root of twenty, and call that x sub one. Then
plug x sub one into the Newton's Method formula for x sub two. Continue this process for x
sub three, four, five, etc, making sure never to round your answer.
You're done when you get two approximations in a row to match each other to eight decimal
places.