SOLUTION: One person says that numbers in radicals are useless because they do not have any real world relevance. Give a convincing practical example to show this person that they are very

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Question 198817: One person says that numbers in radicals are useless because they do not have any real world relevance. Give a convincing practical example to show this person that they are very practical and we need them.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's say that you want to find the distance between two points. You will then use that distance and add it to other distances you find. Also, you want to keep your calculations as exact as possible (to avoid any errors). To keep things exact, you most likely end up with a radical.

For example, let's say that you want to find the distance between the points (1,2) and (5,8):

d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29 Start with the distance formula.


d=sqrt%28%281-5%29%5E2%2B%282-8%29%5E2%29 Plug in x%5B1%5D=1, x%5B2%5D=5, y%5B1%5D=2, and y%5B2%5D=8.


d=sqrt%28%28-4%29%5E2%2B%282-8%29%5E2%29 Subtract 5 from 1 to get -4.


d=sqrt%28%28-4%29%5E2%2B%28-6%29%5E2%29 Subtract 8 from 2 to get -6.


d=sqrt%2816%2B%28-6%29%5E2%29 Square -4 to get 16.


d=sqrt%2816%2B36%29 Square -6 to get 36.


d=sqrt%2852%29 Add 16 to 36 to get 52.


d=2%2Asqrt%2813%29 Simplify the square root.


Now if you found other distances (in terms of radicals), you could add them to this given distance and keep things exact. Once you are done with all of your calculations, you can use a calculator to find the approximate value.