Question

Represent geometrically the following numbers on the number line:

(i) √4.5

(ii) √5.6

(iii) √8.1

(iv) √2.3

Answer 1

(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.

Draw an arc with centre B and radius BD, meeting AC produced at E, then BE = BD = √4.5 units.

(ii) Firstly, we draw a line segment AB = 5.6 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 √5.6 units.

Draw an arc with centre B and radius BD, meeting AC produced at E, then BE = BD = √5.6 units.

(iii) Firstly, we draw a line segment AB = 8.1 units and extend it toC such that SC = 1 unit. Let O be the mid-point of AC.

Now, draw a semi-circle with centre 0 and radius OA

Let us draw BD perpendicular to AC passing through point 6 intersecting the semi-circle at point D:

Hence, the distance BD is √8.1 units .

Draw an arc with centre Sand radius BD, meeting AC produced at E, then BE = BD = √8.1 units.

(iv) Firstly, we draw a line segment AS = 2.3 units and extend it to C such that SC = 1 unit. Let O be the mid-point of AC.

Now, draw a semi-circle with centre 0 and radius OA.

Let us draw BD perpendicular to AC passing through point 6 and intersecting the semi-circle at point D.

Hence, the distance BD is √2.3 units.

Draw an arc with centre 6 and radius BD, meeting AC produced at E, then BE = BD = √2.3 units.