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,
AB2 + BC2 = CA2
22 + 12 = CA2
CA2 = 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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