Represent $\sqrt{5}$ on the number line.

First select a point $O$ on the number line. the corresponding number being $0 .$ Select the appropriate unit and denote the point $A$ on the number line, which represents the number $1.$ Draw segment $AB$ of unit length that is perpendicular to segment $OA.$ Draw segment $OB.$ Now, according to the Pythagoras's theorem $OB =\sqrt{2}$. Draw a segment $BC$ of unit length that is perpendicular to segment $OB.$ Draw segment $OC.$ Now $OC =\sqrt{3}$. Draw a segment $CD$ of unit length that is perpendicular to segment $OC.$ Draw segment $OD.$ Now $OD$ $=\sqrt{4}$. Draw a segment $DE$ of unit length that is perpendicular to segment $OD.$ Draw segment $OE.$ Now $OE =\sqrt{5}.$ Now with $O$ as centre and radius $= OE$, we draw an arc of the circle which intersects the number line at point $P.$ Here. $\sqrt{5}$ is represented by point $P$ on the number line.