Question

Represent $\sqrt{2}$ & $\sqrt{3}$ on the number line

Answer 1

Consider a unit square OABC, with each side 1 unit in length. Then by using pythagoras theorem.

$OB=\sqrt{1+1}=\sqrt{2}$
Now, transfer this square onto the number line making sure that the vertex O coincides with zero

With O as centre & OB as radius, draw an arc, meeting OX. at P. Then
$OB=OP=\sqrt{2}$ units
Then, the point P represents $\sqrt{2}$ on the number line.
Now draw, BC OB such that BC = 1 unit, join OC. Then
$OC=\sqrt{(\sqrt{2}{)}^2+(1{)}^2}=\sqrt{3}$ units

With O as centre & OC as radius, draw an arc, meeting OX at Q. Then
$OQ=OC=\sqrt{3}$ units
Then, the point Q represents $\sqrt{3}$ on the number line.