Question
Represent $\sqrt{5}$ 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 OA = 2 units.
Draw perpendicular AZ at A on the number line and cut-off arc AB = 1 unit.
By Pythagoras Theorem,
OB2 = OA2 + AB2
= 22 + 12 = 4 + 1 = 5
$\Rightarrow\text{OB}=\sqrt{5}$
Taking O as centre and $\text{OB}=\sqrt{5}$ as radius draw an arc cutting real line at C.
Clearly, $\text{OC}=\text{OB}=\sqrt{5}$
Hence, C represents $\sqrt{5}$ on the number line.
On the number line, take point O corresponding to zero.
Now take point A on number line such that OA = 2 units.
Draw perpendicular AZ at A on the number line and cut-off arc AB = 1 unit.
By Pythagoras Theorem,
OB2 = OA2 + AB2
= 22 + 12 = 4 + 1 = 5
$\Rightarrow\text{OB}=\sqrt{5}$
Taking O as centre and $\text{OB}=\sqrt{5}$ as radius draw an arc cutting real line at C.
Clearly, $\text{OC}=\text{OB}=\sqrt{5}$
Hence, C represents $\sqrt{5}$ on the number line.
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