Question

Represent $\sqrt{6},\sqrt{7},\sqrt{8}$ on the number line.

Answer 1

We are asked to represent 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 , so

(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 and

(5) Take A as center and AB₁ as radius and draw an arc which cuts the line AX at A_2.

Here

So

So A₂ is the representation for

(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

So point A₃ is the representation of

(3) Again draw the perpendicular lineto AX

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

Here;

A₄ is basically the representation of