Represent 5–√ on the number line.

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 ⊥⊥ 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 Δ∆OAB,

Using Pythagoras theorem,

$\mathrm{OB}=\sqrt{\mathrm{OA}^{2}+\mathrm{AB}^{2}}$

$=\sqrt{2^{2}+1^{2}}$

$=\sqrt{4+1}$

$=\sqrt{5}$