Question

Locate $\sqrt{2}$ on number line.

Answer 1

At $O$ draw a unit square $OABC$ on number line with each side $1$ unit in length.

By Pythagoras theorem $OB=\sqrt{1^2+1^2}=\sqrt{2}$

We have seen that $OB=\sqrt{2}$. Using a compass with centre $O$ and radius $OB$, draw an arc on the right side to $O$ intersecting the

number line at the point $K$. Now $K$ corresponds to $\sqrt{2}$ on the number line.