Question
Locate $\sqrt{2}$ on the number line.
✓
Answer
Consider a square $OABC$, with each side $1$ unit in length (see Fig.).
Then you can see by the Pythagoras theorem that $OB = \sqrt{1^{2}+1^{2}}=\sqrt{2}$.
Transfer Fig. onto the number line making sure that the vertex $O$ coincides with zero (see Fig.)
We have just seen that $OB = \sqrt{2}$.
Using a compass with centre $O$ and radius $OB$, draw an arc intersecting the number line at the point $P.$
Then P corresponds to $\sqrt{2}$ on the number line.
Then you can see by the Pythagoras theorem that $OB = \sqrt{1^{2}+1^{2}}=\sqrt{2}$.
Transfer Fig. onto the number line making sure that the vertex $O$ coincides with zero (see Fig.)
We have just seen that $OB = \sqrt{2}$.
Using a compass with centre $O$ and radius $OB$, draw an arc intersecting the number line at the point $P.$
Then P corresponds to $\sqrt{2}$ on the number line.
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