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 $AB=8.1units$. 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 $\sqrt{8.1}$.