What are Irrational Numbers?

What are Irrational Numbers?

Now we know that square root of 2 is an Irrational number. If you use a calculator to calculate the value of Root 2 you will get something like 1.4142135 and so on. This value that you get is actually non-terminating. It is never ending. Also, you will not find any pattern in the digits after the decimal. Hence, it’s also called a non-recurring decimal. There is no pattern that occurs again and again. These kinds of numbers are called Irrational numbers. Consider square root of 3 for instance. You will get its value as 1.732050 and so on. Even this decimal is non-terminating and non-recurring. So root 3 is also an Irrational number. You can try calculating the values of root 5, root 6, root 7 or root 8, you will find that all of them result in non-terminating, non-recurring decimals. But wait… root 9 equals 3. This is a Rational number. Yes, root 9 is not an Irrational number. In fact, square root of any perfect square will be a Rational number. But the square root of any number which is not a perfect square will always result in an Irrational number. Here’s the interesting part. If you know these two points well, you can even form an Irrational number by yourself. Let’s see how. We have to form a number which does not end and does not repeat any pattern. Something like 2.01001000100001 and so on. Here, the number does not end and is also non-recurring. This means that there is no pattern that repeats forever. You can even have a number like 15.2349449444944449 and so on This is also Irrational as it is non-terminating and non-recurring. Where does this concept help us? Say your are asked to find two Irrational numbers between 1.23 and 1.25. Remember, 1.24 is incorrect as its terminating. We need a non-terminating, non-recurring decimal. Yes, but we know that 1.24 is between these two numbers. After 1.24 we can start writing 010010001 and so on. That’s one Irrational number between these two numbers. Again, let’s write 1.24 and this time we write 020020002 and so on after it. That’s your second Irrational number. So to find Irrational numbers between two numbers, just write a Rational number between them and then add non-terminating, non-recurring digits after it.

100 thoughts on “What are Irrational Numbers?”

  1. u are great … i have a test in school so I subscribed ur channel and understanding u … Thank you sooo much for that. ..

  2. Are there any irrational numbers that contain more of one digit than another, i.e. the distribution of the ten digits is not uniform?

  3. I was absent the day this concept was taught in school and I had no idea what irrational numbers were. I saw your video and now I have a better understanding than my class fellows!


  4. ((((10 to the 100th power )))))U SOUND LIKE SIRI'S SISTER …wen u said 010010001 (it would be grt if u went so on)…LOL…..

  5. ummmmm. I was trying to relearn how to do this and this ad comes up "sick of searching up math help from 6 years ago" like wtf google

  6. I love how all of you are like "I have a math test tomorrow thx for the help"…. And left it to the last minute to learn something that'll probably only give you two marks out of a how many marker exam 😂

  7. I really appreciate you for making this in English

    I am a non-indian speaking person who is in a Indian school that follows the CBSE system

  8. Sir,can you tell me which application is you use for making these type of videos???
    I have a small youtube educational channel,your answer will help me to improve my channel..
    plz give the name of the software???

  9. you made a mistake when saying square root of imperfect square is irrational because 2.25^1/2 or root 2.25=1.5 which is rational

  10. I searched all over the internet to find a video I understand and I couldn’t find one, but I found this and I actually understand so thank you so much this was really helpful :))

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