Question 198008
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4 \times 4 = 16]


therefore


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{17} > 4]


and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 5 \times 5 = 25]


therefore


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{17} < 5]


Since 16 is a lot closer to 17 than 17 is to 25, let's try 4.1:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4.1 \times 4.1 = 16.81]


a bit small.


Let's try 4.2:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4.2 \times 4.2 = 17.64]


Since 16.81 is closer to 17 than 17 is to 17.64, we can say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4.05 < \sqrt{17} < 4.14]


and therefore


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{17} \approx 4.1] to the nearest tenth.


And the calculator says:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{17} \approx 4.1231056256176605498214098559741]


verifying the result.



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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