represent 2 + root 3 on a number line - Maths - Number Systems

Question

represent 2 + root 3 on a number line

Lalit Mehra · Accepted Answer

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

$\Rightarrow BD = \sqrt{2} units$

Draw DE ⊥ BD such that DE = 1 units. Join BE.

In right ΔBDE,

BE² = BD² + DE² $= (\sqrt{2})^{2} + (1)^{2} = 2 + 1 = 3$

$\Rightarrow BE = \sqrt{3} units$

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.

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