Question

Show how √5 can be represented 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,

OB²=OA²+AB²

OB=(2)²+1²=5

OB=√5

Taking O as the centre and OB=√5 as radius draw an arc cutting real line at C. Clearly, OC=OB= √5

Hence, C represents √5 on the number line.