Question:
Locate $\sqrt{8}$ on the number line.
Solution:
To represent $\sqrt{8}$ on the number line, follow the following steps of construction:
(i) Mark points 0 and 2 as $O$ and $B$, respectively.
(ii) At point $B$, draw $A B \perp O A$ such that $A B=2$ units.
(iii) Join OA.
(iv) With $O$ as centre and radius $O A$, draw an arc intersecting the number line at point $P$.
Thus, point P represents $\sqrt{8}$ on the number line.
Justification:
In right $\triangle \mathrm{OAB}$,
Using Pythagoras theorem,
$\mathrm{OA}=\sqrt{\mathrm{OB}^{2}+\mathrm{AB}^{2}}$
$=\sqrt{2^{2}+2^{2}}$
$=\sqrt{4+4}$
$=\sqrt{8}$