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

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

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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

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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