How to locate $\sqrt{10}$ on the number line.

Given: A number $\sqrt{10}$.

To do: To locate $\sqrt{10}$ on the number line.

Solution: 

Given number $\sqrt{10}=\sqrt{9+1}$

$\Rightarrow \sqrt{10}=\sqrt{3^2+1^2}$

Steps of construction:

$( i)$. Take $OA=3\ unit$ on the number line.   

$( ii)$. Draw a perpendicular on $A$ and draw a line $AB=1\ unit$ 

$( iii)$. Now join $OC$ with $10$. 

$( iv)$. Now take $O$ as center and $OB$ as radius, draw an arc which cuts the number line at point $P$.

$( v)$. $OP=OB=\sqrt{10}$. 

Thus, $OP$ is $\sqrt{10}$ on the number line.

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Updated on: 10-Oct-2022

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