Given to represent **√**3. 5, **√**9. 4, **√**10. 5 on the real number line

Representation of **√**3 .5 on the real number line:

Steps involved:

(i) Draw a line and mark A on it.

(ii) Mark a point B on the line drawn in step - (i) such that AB = 3. 5 units

(iii) Mark a point C on AB produced such that BC = 1unit

(iv) Find mid-point of AC. Let the midpoint be O

=> AC = AB + BC = 3.5 + 1 = 4.5

=> AO = OC = AC/2 = 4.5/2 = 2.25

(v) Taking O as the center and OC = OA as radius drawn a semi-circle. Also draw a line passing through B perpendicular to OB. Suppose it cuts the semi-circle at D. Consider triangle OBD, it is right angled at B.

(vi) Taking B as the center and BD as radius draw an arc cutting OC produced at E. point E so obtained represents **√**3. 5 as BD = BE =**√**3.5 radius Thus, E represents the required point on the real number line.

Representation of **√**9.4 on real number line steps involved:

(i) Draw and line and mark A on it

(ii) Mark a point B on the line drawn in step (i) such that AB =9. 4 units

(iii) Mark a point C on AB produced such that BC = 1 unit.

(iv) Find midpoint of AC. Let the midpoint be O.

=> AC = AB + BC = 9. 4 + 1 = 10 .4 units => AD = OC = AC/2 = 10.4/2 = 5.2 units

(v) Taking O as the center and OC = OA as radius draw a semi-circle. Also draw a line passing through B perpendicular to OB. Suppose it cuts the semi-circle at D. Consider triangle OBD, it is right angled at B.

(vi) Taking B as center and BD as radius draw an arc cutting OC produced at E so obtained represents **√**9 .4 as BD = BE = **√**9.4 = radius Thus, E represents the required point on the real number line.

Representation of **√**10.5 on the real number line:

Steps involved:

(i) Draw a line and mark A on it

(ii) Mark a point B on the line drawn in step (i) such that AB =10 .5 units

(iii) Mark a point C on AB produced such that BC = 1unit

(iv) Find midpoint of AC. Let the midpoint be 0.

=> AC = AB + BC = 10. 5 + 1=11. 5 units

=> AO = OC = AC/2 = 11.5/2 = 5.75 units

(v) Taking O as the center and OC = OA as radius, draw a semi-circle. Also draw a line passing through B perpendicular to DB. Suppose it cuts the semi-circle at D. consider triangle OBD, it is right angled at B

(vi) Taking B as the center and BD as radius draw on arc cutting OC produced at E. pointE so obtained represents **√**10. 5 as BD = BE = **√**10. 5 radius arcsThus, E represents the required point on the real number line