# How to represent irrational numbers on number line

## Representation of irrational numbers on the number line

Irrational numbers are the numbers which have a non terminating and non-repeating decimal expansion. They don’t have any fixed value so we can’t represent them directly on the number line. we have to use a few tricks for this

Before understanding representation of irrational numbers on number line first, we need to understand Pythagoras’ theorem
Pythagoras’ Theorem:: Over 2000 years ago there was an amazing discovery about triangles:
When a triangle has a right angle (90°) and squares are made on each of the three sides then the biggest square has the exact same area as the other two squares put together!

pythagorus theorem

Or
it can simply be written as an equation relating the lengths of the sides a, b and c, like this:

Pythagoras’s theorem

After understanding Pythagoras’ theorem we will learn how to represent an irrational number  on number line
Suppose we want to draw √10 on the number line we will do following steps:
first of all, we need to break 10 as a sum of two numbers which are perfect squares in itself.
for example, 10 can be written as 8+2,7+3,6+4,5+5 but we will prefer it breaking as 9+1 because both 9 and 1 are complete squares.then we do like this:

(√10)²= 10
= 9+1
=(3)²+(1)²
now if we draw a right angled triangle taking one side as 3 unit, another side as 1 unit then hypotenuse will become √10

rep. on number line

We can easily put this value on the number line. Many irrational numbers can be shown on number line using this method
In my next post, I will discuss the numbers which can not be written as a sum of two complete square numbers