Question

Locate $\sqrt{13}$ on the number line.

Answer 1

To represent $\sqrt{13}$ on the number line, follow the following steps of construction:
(i) Mark points $0and3$ as O and B, respectively.
(ii) At point B, draw AB OA such that AB = $2$ units.
(iii) Join OA.
(iv) With O as centre and radius OA, draw an arc intersecting the number line at point P.
Thus, point P represents $\sqrt{13}$ on the number line.

$$\begin{gathered} \mathrm{In}∆\mathrm{AOB}, \\ {\mathrm{OA}}^2={\mathrm{OB}}^2+{\mathrm{AB}}^2 \\ \Rightarrow {\mathrm{OA}}^2=3^2+2^2 \\ \Rightarrow {\mathrm{OA}}^2=9+4 \\ \Rightarrow {\mathrm{OA}}^2=13 \\ \Rightarrow \mathrm{OA}=\sqrt{13} \end{gathered}$$