Represent √5 on the number line.
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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
OB²=(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.
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