Question

Locate $\sqrt{3}$ on a number line.

Answer 1

Locate the given number on on a number line:

Given irrational number, $\sqrt{3}$

We will begin by constructing $\sqrt{2}$

So, $2$ can be written as the sum of square of two natural number

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

So, consider $AB=1units$

Draw a perpendicular to $AB$, draw $BC=1unit$

Now join $AC$

On applying Pythagoras theorem,

We obtain $AC=\sqrt{2}$

Now,

$3$ can be written as the sum of square of two natural number

$$\begin{gathered} 3={\left(\sqrt{2}\right)}^2+1^2 \\ \Rightarrow \sqrt{3}=\sqrt{{\left(\sqrt{2}\right)}^2+1^2} \end{gathered}$$

Draw a perpendicular to $AC$, draw $CD=1unit$

Now join $AD$

On applying Pythagoras theorem,

We obtained $AD=\sqrt{3}$

Draw an arc with centre $A$ and radius $AD$ using compass such that its intersects the number line on the point $E$.

Then, we get, $E$ corresponding to $\sqrt{3}$, or we can say $AE=\sqrt{3}$

Hence, we obtain $\sqrt{3}$ on the number line