Question

Represent geometrically the following number on the number line.

(i) √4.5 (ii) √8.1​

Answer 1

Explanation:

(i) Firstly, we draw a line segment AB = 4.5 units and extend it to C such that BC = 1 unit. Let O be the mid-point of AC. Now, draw a semi-circle with centre O and radius OA Let us draw BD perpendicular to AC passing through point B and intersecting the semi-circle at point D. Hence, the distance BD is √4.5 units.

2)

Presentation of 8.1 on number line:

Mark the distance 8.1 units from a fixed point A on a given line to obtain a point B such that AB=8.1 units. From B, mark a distance of 1 unit and mark the new points as C. Find the mid-point of AC and mark that point as O. Draw a semicircle with a centre O and radius OC. Draw a line perpendicular to AC passing through B and intersecting the semicircle at D. Then, BD=8.1.

Now, draw an arc with centre B and radius BD, which intersects the number line in E. Thus, E represents 8.1.