Draw a line segment of length $\sqrt{8}$ cm.

Steps of construction :

1. Draw a line segment XY.

2. Draw OB = 1 cm which is perpendicular to the line XY at O.

3. From B draw an arc of 3 cm cutting XY at A.

4. Join BA and OA.

So, OAB is the right angle triangle.

By pythagoras theorem,

⇒ AB² = OB² + OA²

⇒ 3² = 1² + OA²

⇒ OA² = 9 - 1

⇒ OA² = 8

⇒ OA = $\sqrt{8}$ cm.

Hence, OA is the required line of $\sqrt{8}$ cm.