Represent `sqrt3.5,` `sqrt9.4,` `sqrt10.5` on the real number line.

#### Solution

We are asked to represent the real numbers `sqrt3.5,` `sqrt9.4` and `sqrt10.5`on the real number line

We will follow a certain algorithm to represent these numbers on real number line

(a) `sqrt3.5`

We will take A as reference point to measure the distance

(1) Draw a sufficiently large line and mark a point A on it

(2) Take a point B on the line such that AB = 3.5 cm

(3) Mark a point C on the line such that BC = 1 cm

(4) Find mid point of AB and let it be O

(5) Take O as center and OC as radius and draw a semi circle. Draw a perpendicular BD which cuts the semi circle at D

(6) Take B as the center and BD as radius, draw an arc which cuts the horizontal line at E

(7) Point E is the representation of `sqrt3.5`

(b) `sqrt9.4`

We will take A as reference point to measure the distance. We will follow the same figure in the part (a)

(1) Draw a sufficiently large line and mark a point A on it

(2) Take a point B on the line such that AB = 9.4 cm

(3) Mark a point C on the line such that BC = 1 cm

(4) Find mid point of AB and let it be O

(5) Take O as center and OC as radius and draw a semi circle. Draw a perpendicular BC which cuts the semi circle at D

(6) Take B as the center and BD as radius, draw an arc which cuts the horizontal line at E

(7) Point E is the representation of `sqrt9.4`

(c) `sqrt10.5`

We will take A as reference point to measure the distance. We will follow the same figure in the part (a)

(1) Draw a sufficiently large line and mark a point A on

(2) Take a point B on the line such that AB = 10.5 cm

(3) Mark a point C on the line such that BC = 1 cm

(4) Find mid point of AB and let it be O

(5) Take O as center and OC as radius and draw a semi circle. Draw a perpendicular BC which cuts the semi circle at D

(6) Take B as the center and BD as radius, draw an arc which cuts the horizontal line at E

(7) Point E is the representation of `sqrt10.5`