=> show how √5 can be represented at a number line
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ANSWER
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,
OB
2
=OA 2 +AB 2
OB 2 =(2)
2 +1 2 =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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