Question

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

Answer 1

It requires a little accuracy to show root 5 on number line.

To represent √5 on the number line, let's consider an integer 5.

We can express 5 as the sum of squares of two numbers.

Now, we have \(5 = 2² + 1²\)

\(⇒ (\sqrt5)^2 = 2² + 1²\)

The above equation follows the Pythagoras theorem with √5 as the hypotenuse, 2 and 1 as the other two sides of the right triangle respectively.

This shows that we need to construct a right triangle with sides 2 units and 1 units so that the hypotenuse becomes √5 units on the number line.

Observe the figure and the steps given below to represent root 5 on the number line. Let us see how to draw root 5 on number line.

Step 1: On the number line, take 2 units from 0 and represent this point as A. Therefore, segment AB = 2 units

Step 2: At point B, draw a perpendicular and mark C such that BC = 1 unit. Join A to C. Using the Pythagoras theorem, we can see that AC is the hypotenuse because ABC is a right-angled triangle and the side opposite to the right angle is the hypotenuse.

In △ABC, using Pythagoras theorem, we have

AC² = AB² + BC²

= 2² + 1²

= 5

∴ AC = √5 units.