Represent $ \sqrt{9.3} $ on the number line.

Given: 

Given number is $\sqrt{9.3}$.

To do: 

We have to represent $\sqrt{9.3}$ on the number line.

Solution:

1. Draw a line segment $AB=9.3$ units.

2. Produce $B$ till point $C$, such that $BC=1$ unit.

3. Find the mid-point of $\mathrm{AC}$, let it be $\mathrm{O}$.

4. Taking $O$ as the centre, draw a semi-circle, passing through $A$ and $C$.

5. Draw a line passing through $B$ perpendicular to $OB$, and cutting semicircle at $D$.

6. Consider $B$ as the centre and $BD$ as the radius and draw an arc cutting $OC$ produced at $E$.

$\mathrm{BD}^{2}=2 \mathrm{OC} \times \mathrm{BC}-(\mathrm{BC})^{2}$

$=2 \times 5.15 \times 1-1$

$=9.3$

$\Rightarrow \mathrm{BD}=\sqrt{9.3}$ 

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Updated on: 10-Oct-2022

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