Question

Locate $\sqrt{3}$ on the number line.

Answer 1

For drawing $\sqrt{3}$

We consider Pythagoras theorem

As $1+2=3$

$1^2+(\sqrt{2}{)}^2=3$ [$\because 1^2=1,(\sqrt{a}{)}^2=a$]

$\sqrt{1^2+(\sqrt{2}{)}^2}=\sqrt{3}$ [taking square root on both sides]

Using Pythagoras theorem

${Hyponenuse}^2={Base}^2+{Height}^2$

$Hyponenuse=\sqrt{{Base}^2+{Height}^2}$

$=\sqrt{1^2+(\sqrt{2}{)}^2}$

$=\sqrt{3}$

First, we will find $\sqrt{2}$ and mark it on our number line, then we will find $\sqrt{3}$

Base $=1$ unit, height $=1$ unit, then hypotenuse $=\sqrt{1^2+1^2}=\sqrt{2}$ units

Drawing $\sqrt{2}$

For $\sqrt{3}$

Base $=\sqrt{2}$ units, Height $=1$ unit, hypotenuse $=\sqrt{(\sqrt{2}{)}^2+1^2}=\sqrt{2+1}=\sqrt{3}$ units

Point $M$ will represent $\sqrt{3}$ on the number line.