Draw a line segment of length √3 cm.

Steps of construction : 1. Draw a line segment XY. 2. Draw OB = 1 cm which is perpendicular to the line XY at point O. 3. From B draw an arc of 2 cm cutting XY at A. 4. Join BA and OA. So, OAB is the right angle triangle. By pythagoras theorem, ⇒ AB 2 = OB 2 + OA 2 ⇒ 2 2 = 1 2 + OA 2 ⇒ OA 2 = 4 - 1 ⇒ OA 2 = 3 ⇒ OA = cm. Hence, OA is the required line of cm.