Question
Locate $\sqrt{8}$ on the number line.
✓
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 $A B=2$ units.
By Pythagoras Theorem, $OB ^2= OA ^2+ AB ^2=2^2+2^2=4+4=8$
$\Rightarrow\text{OB}=\sqrt{8}$
Taking O as centre and $\text{OB}=\sqrt{8}$ as radius draw an arc cutting real line at C.
Clearly, $\text{OC}=\text{OB}=\sqrt{8}$
Hence, C represents $\sqrt{8}$ 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 $A B=2$ units.
By Pythagoras Theorem, $OB ^2= OA ^2+ AB ^2=2^2+2^2=4+4=8$
$\Rightarrow\text{OB}=\sqrt{8}$
Taking O as centre and $\text{OB}=\sqrt{8}$ as radius draw an arc cutting real line at C.
Clearly, $\text{OC}=\text{OB}=\sqrt{8}$
Hence, C represents $\sqrt{8}$ on the number line.
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