Show how can be √5 represented on the number line.

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 unit

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 arc at point which is √5 distance from 0 as it is a radius of the circle with center A

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