Question

Locate $\sqrt{10}$ on the number line.

Answer 1

To represent $\sqrt{10}$ on the number line, follow the following steps of construction:

(i) Mark points 0 and 3 as O and B, respectively.
(ii) At point A, draw AB ⊥$\perp$ OA such that AB = 1 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 $\sqrt{10}$ on the number line.

Justification:

In right Δ$∆$OAB,

Using Pythagoras theorem,

$$\begin{gathered} \mathrm{OA}=\sqrt{{\mathrm{OB}}^2+{\mathrm{AB}}^2} \\ =\sqrt{3^2+1^2} \\ =\sqrt{9+1} \\ =\sqrt{10} \end{gathered}$$