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how to represent root3 on a numberline
let x 'ox be a horizontal line taken as x axis ant let O be the origin

take OA = 1 unit and draw AB perpandicular OA such as that AB = 1 unit

join OB=root over OA2+AB2 = root over12+12= root over 2 unit

with O as centre and OB as radius,draw on arc,meeting OX at P.

Then OP=OB=root over 2 units.

Thus the point P represent root over 2 on a real no. line

now, draw BC perpendicular OB such that BC = 1 unit .

Join OC Then,

OC=root over OB2+BC2 = root over (root 2)2+12=root3 units.

With Oas centre and OC as radius ,draw an arc , meeting OX at Q.Then

OQ=OC=root 3 units.

Hence point Q represent root 3.


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