Question 3
Show how √5 can be represented on the number line.
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. Join CA.
Step 3: Now, ABC is a right angled triangle. Applying 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 a centre draw an arc touching the number line. The point at which number line get intersected by the arc is at √5 distance from 0 because it is a radius of the circle whose centre is A.
Thus, √5 is represented on the number line as shown in the figure.