show how √ 5 can be presented on the number line??
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Step-vise-step explanation
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,
[tex] {ob}^{2} = {oa}^{2} + {ab}^{2} \\ {ob}^{2} = {2}^{2} + {1}^{2} = 5 \\ {ob}^{2} = \sqrt{5} [/tex]
Taking O as the centre and OB= root 5 as radius draw an arc cutting real line at C. Clearly, OC=OB= root5
[tex]hence \: c \: represents \: \sqrt{5} on \: the \: number \: line[/tex]
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