Question
Locate $\sqrt{10}$ 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 $O A=3$ units.
Draw perpendicular $A Z$ at $A$ on the number line and cut-off arc $A B=1$ unit.
By Pythagoras Theorem, $OB ^2= OA ^2+ AB ^2=3^2+1^2=9+1=10$
$\Rightarrow\text{OB}=\sqrt{10}$
Taking O as centre and $\text{OB}=\sqrt{10}$ as radius draw an arc cutting real line at C.
Clearly, $\text{OC}=\text{OB}=\sqrt{10}$
Hence, C represents $\sqrt{10}$ on the number line.
Draw perpendicular $A Z$ at $A$ on the number line and cut-off arc $A B=1$ unit.
By Pythagoras Theorem, $OB ^2= OA ^2+ AB ^2=3^2+1^2=9+1=10$
$\Rightarrow\text{OB}=\sqrt{10}$
Taking O as centre and $\text{OB}=\sqrt{10}$ as radius draw an arc cutting real line at C.
Clearly, $\text{OC}=\text{OB}=\sqrt{10}$
Hence, C represents $\sqrt{10}$ on the number line.
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