√4.5

Mark the distance 4.5 units from a fixed point A on a given line to obtain a point B such that AB = 4.5 units.

From B, mark a distance of 1 unit and mark the new point as C.

Find the mid-point of AC and mark that point as O. Draw a semicircle with centre O and radius OC.

Draw a line perpendicular to AC passing through B and intersecting the semicircle at D. Then, BD = √4.5.

Draw an arc with centre B and radius BD, meeting AC produced at E, then BE = BD = √4.5 units.