Question
Represent $\sqrt{4.7}$ geometrically on the number line.
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Answer
Draw a line segment $AB = 4.7$ units and extend it to $C$ such that $BC = 1$ unit.
Find the midpoint $O$ of $AC$. With $O$ as centre and $OA$ as radius, draw a semicircle.
Now, draw $\text{BD}\perp\text{AC},$ intersecting the semicircle at $D$.
Then, $\text{BD}=\sqrt{4.7}\text{units}.$ With $B$ as centre and $BD$ as radius, draw an arc, meeting $AC$ produced at $E$.
Then, $\text{BE}=\text{BD}=\sqrt{4.7}\ \text{units}.$
Find the midpoint $O$ of $AC$. With $O$ as centre and $OA$ as radius, draw a semicircle.
Now, draw $\text{BD}\perp\text{AC},$ intersecting the semicircle at $D$.
Then, $\text{BD}=\sqrt{4.7}\text{units}.$ With $B$ as centre and $BD$ as radius, draw an arc, meeting $AC$ produced at $E$.
Then, $\text{BE}=\text{BD}=\sqrt{4.7}\ \text{units}.$
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