Show how $\sqrt{5}$ can be represented on the number line.

(N/A) To represent $\sqrt{5}$ on the number line,we use the Pythagorean theorem: $\sqrt{5} = \sqrt{2^2 + 1^2}$.
$1$. Draw a number line and mark a point $O$ representing $0$ and a point $A$ representing $2$ units from $O$.
$2$. At point $A$,construct a perpendicular line segment $AB$ of length $1$ unit.
$3$. Join $O$ and $B$. In the right-angled triangle $\triangle OAB$,by the Pythagorean theorem:
$OB^2 = OA^2 + AB^2$
$OB^2 = 2^2 + 1^2 = 4 + 1 = 5$
$OB = \sqrt{5}$
$4$. Now,with $O$ as the center and $OB$ as the radius,draw an arc that intersects the number line at point $C$.
$5$. The distance $OC$ is equal to $OB$,which is $\sqrt{5}$. Thus,point $C$ represents $\sqrt{5}$ on the number line.