Question

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

Answer 1

To represent $\sqrt{5}$ on the number line, follow the following steps of construction:

(i) Mark points 0 and 2 as O and P, respectively.
(ii) At point A, draw AB $\perp$ OA such that AB = 1 units.
(iii) Join OB.
(iv) With O as centre and radius OB, draw an arc intersecting the number line at point P.
Thus, point represents $\sqrt{5}$ on the number line.

Justification:

In right $∆$OAB,

Using Pythagoras theorem,

$$\begin{gathered} \mathrm{OB}=\sqrt{{\mathrm{OA}}^2+{\mathrm{AB}}^2} \\ =\sqrt{2^2+1^2} \\ =\sqrt{4+1} \\ =\sqrt{5} \end{gathered}$$