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.
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.