Question

Represent geometrically the following numbers on the number line: $\sqrt{2.3}$

Answer 1

Step 1: General steps to construct square root of a number:

Let $N$ be the number whose square root has to be constructed. To do so,

1. Construct a line segment with length $N$.
2. Extend the line segment by $1$ unit.
3. Draw semicircle with diameter as the $N+1$ unit segment.
4. Draw a perpendicular onto the circle from the point where the $1$ unit segment was extended from.
5. The length of the perpendicular will be $\sqrt{N}$.

Step 2: Construct the given number

Given number is, $\sqrt{2.3}$

Draw a line segment $AB$ with length $5.6$ units.

Extend $B$ by $1$ unit and mark the point as $C$

Mark $O$ on $AC$ such that $OA=OC$

Draw a semicircle centered at $O$ passing through $A$ and $C$

Draw a perpendicular from $B$ onto the semicircle and mark it as $D$.

Measure $BD$ with a compass and draw an arc from $D$ centered at $B$ until it is collinear to $AC$

Thus, $\sqrt{2.3}$ is constructed.