Question

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

Answer 1

Draw number line as shown in the figure. Let the point O represent 0(zero) and point A represents 2. Draw perpendicular $AX$ at $A$ on the number line and cut-off arc $AB=1unit.$

We have $OA=2$ units and $AB=1unit$

Using pythagoras theorem, we have,

$O{B}^2=O{A}^2+A{B}^2$

$O{B}^2=(2{)}^2+1^2=5$

$OB=\sqrt{5}$

Taking $O$ as the centre and $OB=\sqrt{5}$ as radius draw an arc cutting real line at $C.$ Clearly, $OC=OB=$$\sqrt{5}$.

Hence, C represents $\sqrt{5}$ on the number line.