Show how $ \sqrt{5} $ can be represented on the number line.

For representing any irrational number $sqrt{n}$ on the number line , the representation of $sqrt{n-1}$ can be used.

To represent $sqrt{5}$, use the representation of  $sqrt{5-1} =sqrt{4} =2$.

Draw a perpendicular AB of length 1 unit at A=2 and join OB.

OB$=sqrt{2^{2} +1^{2}} =sqrt{4+1} =sqrt{5}$

Using compass and radius as length of OB, plot point C on the number line such that OC=OB=$sqrt{5}$

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Updated on: 10-Oct-2022

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