Question

Represent √3.5, √9.4, √10.5 on the real number line.

Answer 1

Represent √3.5 on number line 

Step 1: Draw a line segment AB = 3.5 units 

Step 2: Produce B till point C, such that BC = 1 unit 

Step 3: Find the mid-point of AC, say O. 

Step 4: Taking O as the centre draw a semi circle, passing through A and C.

Step 5: Draw a line passing through B perpendicular to OB, and cut semicircle at D.

Step 6: Consider B as a centre and BD as radius draw an arc cutting OC produced at E.

In right ΔOBD,

BD² = OD² – OB² 

= OC² – (OC – BC)² 

(As, OD = OC) 

BD² = 2 OC x BC – (BC)² 

= 2 x 2.25 x 1 – 1

= 3.5 

=> BD = √3.5

Represent √9.4 on number line 

Step 1: Draw a line segment AB = 9.4 units 

Follow step 2 to Step 6 mentioned above.

BD² = 2OC x BC – (BC)² 

= 2 x 5.2 x 1 – 1 

= 9.4

=> BD = √9.4

Represent √10.5 on number line 

Step 1: Draw a line segment AB = 10.5 units 

Follow step 2 to Step 6 mentioned above, we get

BD² = 2OC x BC – (BC)² 

= 2 x 5.75 x 1 – 1

= 10.5 

=> BD = √10.5

Answer 2

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