how can we draw a nuber line?

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how can we draw a nuber line?

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I suppose we can use the ruler, scale, protractor, compass...

there are possibly two ways.

*2² + 2² = 8 = (√8)² *

So construct a right angle triangle with two sides equal to 2 units, then the hypotenuse will be of √8 units.

Draw a long horizontal line AD. Draw a perpendicular AE at A. Bisect the angle DAE to draw the line AF which is at 45⁰ to AD. Now with compass measure 2 units and draw an arc with center A intersecting AF at B. So AB = 2 units.

Now with B as the center and with compass draw an arc cutting AD at C. So BC = 2 units. Thus*we get AC = √8 units - on the horizontal real line.*

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*2nd way*

*3² - 1² = 8 = (√8)² *

construct a right angle triangle with a side = 1 unit, and the hypotenuse = 3 units, then the other side is √8 units.

Draw a long horizontal line AD. At point A, draw AE vertically at 90° to AD. Now with compass set = 1 unit, draw an arc with center A to cut AE at B. So AB = 1.

You may use the compass, protractor and ruler, right? Now, measure 3 units with the compass. Draw an arc with center as B, to cut AD at C. So AC = 3 units.*Thus BC = √8 units on the horizontal real number line.*

there are possibly two ways.

So construct a right angle triangle with two sides equal to 2 units, then the hypotenuse will be of √8 units.

Draw a long horizontal line AD. Draw a perpendicular AE at A. Bisect the angle DAE to draw the line AF which is at 45⁰ to AD. Now with compass measure 2 units and draw an arc with center A intersecting AF at B. So AB = 2 units.

Now with B as the center and with compass draw an arc cutting AD at C. So BC = 2 units. Thus

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construct a right angle triangle with a side = 1 unit, and the hypotenuse = 3 units, then the other side is √8 units.

Draw a long horizontal line AD. At point A, draw AE vertically at 90° to AD. Now with compass set = 1 unit, draw an arc with center A to cut AE at B. So AB = 1.

You may use the compass, protractor and ruler, right? Now, measure 3 units with the compass. Draw an arc with center as B, to cut AD at C. So AC = 3 units.