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

(N/A) $1$. Select a point $O$ on the number line representing $0$.
$2$. Select a unit length and mark point $A$ on the number line at distance $1$ from $O$.
$3$. Draw a perpendicular segment $AB$ of unit length ($1$ unit) at point $A$.
$4$. Join $OB$. By Pythagoras's theorem,$OB = \sqrt{OA^2 + AB^2} = \sqrt{1^2 + 1^2} = \sqrt{2}$.
$5$. Draw a perpendicular segment $BC$ of unit length at point $B$. Join $OC$. Then $OC = \sqrt{OB^2 + BC^2} = \sqrt{(\sqrt{2})^2 + 1^2} = \sqrt{3}$.
$6$. Draw a perpendicular segment $CD$ of unit length at point $C$. Join $OD$. Then $OD = \sqrt{OC^2 + CD^2} = \sqrt{(\sqrt{3})^2 + 1^2} = \sqrt{4} = 2$.
$7$. Draw a perpendicular segment $DE$ of unit length at point $D$. Join $OE$. Then $OE = \sqrt{OD^2 + DE^2} = \sqrt{2^2 + 1^2} = \sqrt{5}$.
$8$. With $O$ as the center and $OE$ as the radius,draw an arc that intersects the number line at point $P$.
$9$. The point $P$ on the number line represents $\sqrt{5}$.