Question

How to plot $\sqrt{6}$ on the number line?

Answer 1

Following steps are performed to plot $\sqrt{6}$ on the number line

From Pythagoras theorem $\sqrt{6}$ can be represented by

$\sqrt{6}=\sqrt{{\left(\sqrt{5}\right)}^2+1^2}$

From Pythagoras theorem $\sqrt{5}$can be represented by

$\sqrt{5}=\sqrt{2^2+1}$

1. Point $A$ is marked on the line at $0$ and $B$ at $2$ so that $AB=2\mathrm{unit}$
2. Draw a line $BC=1\mathrm{unit}$ which is perpendicular to $AB$
3. Now join $AC$ and we get $AC=\sqrt{5}$
4. Draw a line $CD=1\mathrm{unit}$ which is perpendicular to $AC$
5. Now join $AD$ and we get $AD=\sqrt{6}$
6. Draw a circle with $A$ as center and $AD$ as radius it meets $E$
7. Finally, $AE$ represents the $\sqrt{6}$ on the number line

Hence, following steps are performed to plot $\sqrt{6}$ on number line.