**Irrational numbers on the number line**

Irrational numbers are the numbers that 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. Our **IB Maths Tutors** have to use a few tricks for this

Before understanding the representation of irrational numbers on number line first, Our **Online Maths Tutors**, first explain **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!

### OrIrrational Numbers using Pythagoras theorem

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

After understanding Pythagoras’ theorem we will learn how to represent an irrational number on a number line

Suppose we want to draw √10 on the number line we will do the following steps:

first of all, we need to break 10 as a sum of two numbers which are perfect squares in themselves.

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 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

We can easily put this value on the number line. Many irrational numbers can be shown on the number line using this method

In the next post,** IB Online Tutors** will discuss the numbers which can not be written as a sum of two complete square numbers

You can ask your doubts in the comments section. Our tutors will answer them for free asap.

This article is written by Mr. Faisal Khan. He is a well-known faculty of Mathematics in South Delhi. He has more than 18 years of experience working as a Mathematics teacher with the top-most schools of Delhi, NCR. He is currently working as a senior Mathematics Faculty with** Hindustan Times Learning Centres Pvt. Ltd**

very useful article but it will be good if you take difficult number as example