Question

Locate $\sqrt{10}$ on number line.

Answer 1

Step 1. Draw a line segment $OA$of $3unit$ on number line

Given number, $\sqrt{10}$

$10$ can be written as the sum of square of two natural number

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

Therefore on number line

Consider $OA=3units$

Step 2. Draw a perpendicular $AB=1unit$ on $A$

Step 3. Join $OB$

Step 4. Draw an arc with centre $O$ and radius $OB$

On applying Pythagoras theorem,

We obtain $OB=\sqrt{10}$

Draw an arc with centre $O$ and radius $OB$ using compass such that its intersects the number line on the point $C$.

Then, we get, $C$ corresponding to $\sqrt{10}$, or we can say $OC=\sqrt{10}$

Hence, we obtain $\sqrt{10}$ on number line