Question

Represent geometrically the following number on the number line:
$$\sqrt {8.1}$$.

Answer 1

Presentation of $$\sqrt {8.1}$$ on number line:
Mark the distance $$8.1$$ units from a fixed point $$A$$ on a given line to obtain a point $$B$$ such that $$AB = 8.1\ units$$. From $$B$$, mark a distance of $$1$$ unit and mark the new points as $$C$$. Find the mid-point of $$AC$$ and mark that point as $$O$$. Draw a semicircle with a centre $$O$$ and radius $$OC$$. Draw a line perpendicular to $$AC$$ passing through $$B$$ and intersecting the semicircle at $$D$$. Then, $$BD = \sqrt {8.1}$$.
Now, draw an arc with centre $$B$$ and radius $$BD$$, which intersects the number line in $$E$$. Thus, $$E$$ represents $$\sqrt {8.1}$$.