Question
Represent $\sqrt{10.5}$ on the number line.
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Answer
Draw a line segment $OB = 10.5$ units and extend it to $C$ such that $BC = 1$ unit.
Find the midpoint $D$ of $OC$. With $D$ as centre and $DO$ as radius, draw a semicircle.
Now, draw $\text{BE}\perp\text{AC},$ intersecting the semicircle at $E$.
Then, $\text{BE}=\sqrt{10.5}\ \text{units}.$ With $B$ as centre and $BE$ as radius, draw an arc, meeting $AC$ produced at $F$.
Then, $\text{BF}=\text{BE}=\sqrt{10.5}\text{units}.$
Find the midpoint $D$ of $OC$. With $D$ as centre and $DO$ as radius, draw a semicircle.
Now, draw $\text{BE}\perp\text{AC},$ intersecting the semicircle at $E$.
Then, $\text{BE}=\sqrt{10.5}\ \text{units}.$ With $B$ as centre and $BE$ as radius, draw an arc, meeting $AC$ produced at $F$.
Then, $\text{BF}=\text{BE}=\sqrt{10.5}\text{units}.$
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