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**Abbas0000****Member**- Registered: 2017-03-18
- Posts: 29

I searched a lot about it but I haven't found a thing! I were assuming that you guys can help me. The question is just what I wrote in title ((Represent sqrt{2}+sqrt{3} on a number line)).what that make this diffrent is that it's not like adding an rational to irrational because there you had a certain start point and you draw a triangle and it would be done but in the problem that I mentioned when you draw first triangle you will have a point that doesn't exist((it's value is not accurate))! And therefore it's stupidness to draw another triangle from that point.Then, what to do?

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**alter ego****Member**- Registered: 2012-03-30
- Posts: 19

Hi Abbas 0000

What are you accepting as a 'representation'? If you draw a line and Mark points at regular intervals, labelling them 1, 2, 3, etc you have to assume you can do that accurately. In Euclidean geometry we assume you can, but in the real world there is no such thing as perfect accuracy. Pencil drawn points have size and, by viewing under magnification, you will reveal that drawings are never exact.

So I think what you have described is acceptable. Draw a unit line from zero to point A and then a vertical line up of one unit to point B. With compass point at zero and radius OB make an arc to cut the number line at C. OC is root 2.

This point is as accurate as A, so if the point for 1 is acceptable so is C.

Draw a line vertically up from C one unit, to point D. Compass set to radius OD and make an arc to cut the number line at E. This is root 3.

Repeat the root 2 construction from point E and F will be at root 2 + root 3.

Alter

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**Abbas0000****Member**- Registered: 2017-03-18
- Posts: 29

Thank you for answering. I'm saying that the second start point((suppose you've drawn sqrt{2} and this point is the second start point)) would not be exact. then, as you know we can't use pythagorean theorem because we can't say that we draw a line with size of A from a certain origin and then we can't have a triangle with a horizontal line in length of something wanted and therefore there would not be a hypotenuse in length of like sqrt{3} or something else.

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**alter ego****Member**- Registered: 2012-03-30
- Posts: 19

But what does 'exact' mean? If you draw a line 1 inch (or cm) long is that exact? Suppose you look at the line through a magnifying glass. How do you know it is not actually 0.99999 ? I think you are creating an unnecessary difficulty.

A

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**Abbas0000****Member**- Registered: 2017-03-18
- Posts: 29

I think you're right. Thanks any way

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