Question

show on number line 2 + under root 3

Answer 1

To represent
$2 + \sqrt{3}$
on the number line l, firstly mark the points O, A, B and C on l such that OA = AB = BC = 1.

Draw CD ⊥ l such that CD = 1 unit. Join BD.

In right ΔBCD,

BD2 = BC2 + CD2 = 12 + 12 = 1 + 1 = 2

$bd = \sqrt{2 \: \:} \: units$
Draw DE ⊥ BD such that DE = 1 units. Join BE.

In right ΔBDE,

BE2 = BD2 + DE2

$( \sqrt{2} )sqaure + (1)sqaure = 2 + 1 \\ = 3 \\ be = 3units$
Taking B as centre and BE as radius, draw an arc which intersects l in F.

$be = bf = \sqrt{3}$
Here, OB = 2 and
$bf = \sqrt{3}$
$of = ob + bf = \\ 2 + \sqrt{3}$

So, the point F represents
$2 + \sqrt{3}$
on the number line.

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