Question

Represent the numbers $\sqrt{5}$ and $\sqrt{10}$ on a number line.

Answer 1

(i) $\text{Steps of construction for}\sqrt{5}$

Step 1: Draw a number line. Mark $O$ as the zero on the number line.

Step 2: At point $A$, draw $AB\perp OA$ such that $AB=1$ unit.

Step 3: With point $O$ as the centre and radius $OB$, draw an arc intersecting the number line at point $P$.

Thus, $P$ is the point for $\sqrt{5}$ on the number line.

(Refer image: Pic 3.1)

(i) $\text{Steps of construction for}\sqrt{10}$

Step 1: Draw a number line. Mark $O$ as the zero on the number line.

Step 2: At point $A$, draw $AB\perp OA$ such that $AB=1$ unit.

Step 3: With point $O$ as the centre and radius $OB$, draw an arc intersecting the number line at point $C$.

Thus, $C$ is the point for $\sqrt{10}$ on the number line.

(Refer image: Pic 3.2)