Question

Locate $\sqrt{10}$ on number line

Answer 1

We can do it by using Pythagoras Theorem.

We can write $\sqrt{10}$ as follows:

$\sqrt{10}=\sqrt{9+1}\Rightarrow \sqrt{10}=\sqrt{3^2+1^2}$

The construction steps are as follows:

1. Take a line segment $AO=3$ unit on the $x$-axis. (consider $1$ unit = $2$ cm)

2. Draw a perpendicular on $O$ and draw a line $OC=1$ unit

3. Now join $AC$ with $\sqrt{10}$.

4. Take $A$ as center and $AC$ as radius, draw an arc which cuts the $x$-axis at point $E$.

5. The line segment $AC$ in the below diagram represents $\sqrt{10}$ units.