Question
Represent $\sqrt{5}$ on the number line.
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Answer
Draw a number line as shown. On the number line, take point $O$ corresponding to zero.
Now take point $A$ on number line such that $O A=2$ units.
Draw perpendicular $A Z$ at $A$ on the number line and cut-off arc $A B=1$ unit.
By Pythagoras Theorem,
$O B^2=O A^2+A B^2$
$=2^2+1^2$
$=4+1=5$
$\Rightarrow O B=\sqrt{5}$
Taking O as centre and $OB =\sqrt{5}$ as radius draw an arc cutting real line at C .
Clearly, $OC = OB =\sqrt{5}$
Hence, C represents $\sqrt{5}$ on the number line.
Now take point $A$ on number line such that $O A=2$ units.
Draw perpendicular $A Z$ at $A$ on the number line and cut-off arc $A B=1$ unit.
By Pythagoras Theorem,
$O B^2=O A^2+A B^2$
$=2^2+1^2$
$=4+1=5$
$\Rightarrow O B=\sqrt{5}$
Taking O as centre and $OB =\sqrt{5}$ as radius draw an arc cutting real line at C .
Clearly, $OC = OB =\sqrt{5}$
Hence, C represents $\sqrt{5}$ on the number line.
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