Question

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

Answer 1

(i) 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.



(ii) 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.