) Initially mark a horizontal line, let it be number line. Mark a point O on it; then mark OA one unit on this line.
ii) At O erect a perpendicular to the number line; here again mark OB equals one unit.
iii) Join AB; with A as center and AB as radius mark cut off an arc on the number line at C.
So AC equals √2.
Since by construction, OAB is a right triangle, with AB as hypotenuse.
Applying Pythagoras theorem, AB² = OA² + OB²
Each of OA & OB being one unit by construction.
AB² = 1 + 1 = 2
==> AB = √2 units.
Thus AC = √2 units.