Answer :

Steps of construction:

**Step 1:** Let AB be a line of length 2 unit on the number line.

**Step 2:** At B, draw a perpendicular line BC of length 1 unit and then join CA.

**Step 3:** Now, ABC is a right angled triangle.

Using Pythagoras theorem,

AB^{2} + BC^{2} = CA^{2}

2^{2} + 1^{2} = CA^{2}

CA^{2} = 5

CA = √5

Thus, CA is a line of length √5 units.

**Step 4:** Taking CA as a radius and A as the center, construct an arc touching the number line.

The number line gets intersected by the arc at a point which is at √5 distance from 0, as it is a radius of the circle with center A

Thus, √5 is represented on the number line as shown in the figure below.

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