Science:Math Exam Resources/Courses/MATH102/December 2019/Question 03
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Question 03 

Use two iterations of Newton's Method to find a rational number closely approximating . Explain your choice of . You may leave your final answer in calculatorready form. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Find a simple function (for example, an integervalued polynomial) such that is a solution of . 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. We take and . (We choose this because and are easy to evaluate, and clearly .) Then . We use Newton's method:
The final answer is
