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 ⊥ 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 ⊥ 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.