) 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. Proof: 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.