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Show how √5 can be represented on the number line.
Here we write by 5 = (2)2 + 1.
First draw a number line. Construct a right angled ΔOAB on the number line by taking OA = 2 units and AB = 1 unit.
In ΔAOB,
OB = √OA2+ AB2 [From Pythagoras Theorem]
= √(2)2+ (1)2 = √5
Taking O as the centre and OB as the radius mark an arc with the help of compass which intersects the number line at point C.
OC = OB = √5
Hence, point C is represented on the number line.
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