Question

Locate $\sqrt{3}$ on number line

Answer 1

Construct $BD$ of $1$ unit length perpendicular to $OB$ as fig. Join $OD$

By Pythagoras theorem, $OD=\sqrt{(\sqrt{2}{)}^2+1^2}=\sqrt{2+1}=\sqrt{3}$

Using a compass, with centre $O$ and radius $OD$, draw an arc which

intersects the number line at the point $L$ right side to $0$. Then

${}^{\prime }{L}^{\prime }$ corresponds to $\sqrt{3}$. From this we can conclude that many

points on the number line can be represented by irrational numbers also.

In the same way, we can locate $\sqrt{n}$ for any positive integers $n$, after $\sqrt{n-1}$ has been located.