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Represent `Sqrt6,` `Sqrt7,` `Sqrt8` on the Number Line. - CBSE Class 9 - Mathematics

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Question

Represent `sqrt6,` `sqrt7,` `sqrt8` on the number line.

Solution

We are asked to represent `sqrt6,` `sqrt7` and `sqrt8`on the number line

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

We will consider point A as reference point to measure the distance

(1) First of all draw a line AX and YY’ perpendicular to AX

(2) Consider AO = 2 unit and OB = 1 unit, so

`AB=sqrt(2^2+1^2)=sqrt5`

(3) Take A as center and AB as radius, draw an arc which cuts line AX at A1

(4) Draw a perpendicular line A1B1 to AX such that A1B1 = 1 unit and 

(5) Take A as center and AB1 as radius and draw an arc which cuts the line AX at A2.

Here 

AB1 = AA2

`=sqrt("AA"_1^2+A_1B_1^2)`

`=sqrt((sqrt5)^2+1)`

`=sqrt6` unit

So AA2 = `sqrt6` unit

So A2 is the representation for `sqrt6`

(1) Draw line A2B2 perpendicular to AX

(2) Take A center and AB2 as radius and draw an arc which cuts the horizontal line at A3 such that 

AB2 = AA3

`=sqrt("AA"_2^2+A_2B_2^2)`

`=sqrt((sqrt6)^2+1)`

`=sqrt7` unit

So point A3 is the representation of `sqrt7`

(3) Again draw the perpendicular line A3B3 to AX

(4) Take A as center and AB3 as radius and draw an arc which cuts the horizontal line at A4 

Here;

AB3 = AA4

`=sqrt("AA"_3^2+A_3B_3^2)`

`=sqrt((sqrt7)^2+1^2)`

`=sqrt8` unit

A4 is basically the representation of `sqrt8`

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Solution Represent `Sqrt6,` `Sqrt7,` `Sqrt8` on the Number Line. Concept: Representing Real Numbers on the Number Line.
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