Q. 34.1( 730 Votes )

Show how √5

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,

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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