Represent geometrically numbers on the number line:

$\sqrt{4.5}$

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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 $1$ units and mark the new points as $C$. Find the mid-point of $AC$ and mark that points 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, $BD =\sqrt{4.5}.$

Now, draw an arc with centre $B$ and radius $BD$, which intersects the number line in $E$. Thus, $E$ represent $\sqrt{4.5}$

1099-s58

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