Represent geometrically numbers on the number line:

$\sqrt{8.1}$

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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 $0 .$ 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, $B D=\sqrt{8.1}$.

Now, draw an arc with centre $B$ and radius $BD$, which intersects the number line in $E$. Thus, E represents $\sqrt{8.1}$

1099-s60

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