Are you looking for the answer to **Prove That Root 3 is an Irrational Number**, then this article is only for you because I will tell you the solution as well as teach you how to solve this type of question?

This question is given in the NCERT book of class 10th Maths, the answer which every student wants to know. I will not only tell you but also solve it and explain it step by step so that you can understand it and you can do it well in the exam.

It comes in five marks in the board exam, so you guys should strengthen your grip on this type of questions because in the board exam your question paper will come that *Prove That Root 3 is an Irrational Number Class 10th NCERT Math Solutions* which will be of five marks and this The question will make your result better.

This type of question come not only in board exams but also in all competitive exams, so this question is necessary for every student. If you read it completely, then I can say with the full claim that there will be no doubt in your mind till the end and you will solve such questions in a jiffy.

Before going to the question here, you people should know what are rational numbers and irrational numbers, then first of all we will know the meaning of these two words, and after that, we will solve our question.

**Rational Number:** Dear students rational number we call that number which is in the form of a divide but the condition is that there should not be a zero in the denominator, in other languages rational number is the number which remains in the form of q divided p but q not equal to zero.

**Irrational Number:** Now let’s talk about what is an irrational number, then an irrational number is a number which is not a rational number, that is to say, that which does not remain in the form of P divided by Q is an irrational number.

**How to Prove That Root 3 is an Irrational Number by Contradiction Method**

Dear students, today we will learn that **How to Prove That Root 3 is an Irrational Number by Contradiction Method **which is very easy to solve this type of question and it is also fun because we do something in this way first we try to solve it considering it as a rational number. Let’s do this and if we find this statement wrong, then it will automatically prove that this number is not a rational but irrational number.

**Solutions:** We have to prove 3 is an irrational number

Let us assume the opposite,√3 is a rational number

So √3 can be written in the form of a/b, Where a and b (b ≠ 0) are co-prime

Therefore we can find two integers a and b where b ≠ 0, such that

So, √3 = a/b

Now, Squaring on both sides then

(√3)² = (a/b)²

3 = a²/b²

3b² = a² ———– Equation (1)

∴ a² is divisible by 3, so, a is also divisible by 3

again let a = 3c, and putting this value in equation (1) we have –

∴ 3b² = a²

3b² = (3c)²

3b² = 9c²

b² = 9c²/3

b² = 3c²

∴ b² is divisible by 3, So b is also divisible by 3

So, a and b both are divisible by 3, therefore we can say that a and b have at least 3 as a common factor. this contradicts the fact a and b are co-prime numbers. It happens due to the incorrect assumption that √3 is a rational number. So, Root 3 is an Irrational Number that Proved

So dear students, you have seen how easily I solved your question **“Prove That Root 3 is an Irrational Number”**. You should practice such questions as much as possible because it comes up a lot in board exams.

In the previous article, I solved the correct answer of From a Solid Cylinder Whose Height is 2.4 cm in a very simple way. You, people, can also see that because it is very important for all the questions of the NCERT math solutions board exam.

I hope that you will be told anytime now that Prove That Root 3 is an Irrational Number, and then you can prove it very easily through the medium given above.

**How to Prove That Root 3 is an Irrational Number by using the long Division Method**

Dear students, now we will know the correct answer of using long division method to prove that root 3 is an irrational number and not only we will solve it but we will also understand this method how it is done.

If you know this well once, then you will be able to solve any type of question of this type very easily. I am going to tell you to step by step in the right way how to prove root 3 as an irrational number, that too by adopting long division method.

Dear students, above you, can see how root 3 has been proved to be an irrational number of using long division method. In the same way, you people will write your solution in your board exam. Mostly this method is not asked in the exam, yet you should keep it ready.

Dear students Root 3 is an Irrational Number by using long division method, the value of √3 keeps on coming around 1.732… which means that after a time its division starts repeating.

**So the value is √3 = 1.73205080757**

We use it in many places considering it as direct. You must also have calculated by keeping the value of root 3 directly as 1.732 in many questions, it makes the calculation easier.

In the end: Dear students, the answer to today’s question ends here. I hope that you have understood **“Prove That Root 3 is an Irrational Number”** very well, I have shown this question by solving both Contradiction and Long Division Methods. Now you people will be able to solve this type of question very easily, that too without any doubt because I have explained it to you in a very easy way.

**FAQs Related Prove That Root 3 is an Irrational Number**

### Is √ 3 is an irrational number?

Yes, √ 3 is an irrational number, I have explained its complete Math solutions to you in this article. We have solved this type of question in two ways, you can read more deeply in the above article.

### Is ✓ 3 a rational or irrational number?

✓ 3 is an irrational number, not a rational number, we had understood this very easily above. To solve this type of question, we first assume the opposite, and then by proving it wrong, we prove that the statement before it is true.

### Is √ 3 a real number?

If you want to know is √ 3 a real number? So the correct answer is Yes. Root 3 is a real number because only rational and irrational numbers are called real numbers.

### How do you prove a root number is rational or irrational?

How to prove a number to be rational and how to make it irrational, we have taught it in a very good way through today’s article. We solve the opposite value of what has been said in the question, and then by proving it wrong, we prove the statement before it to be true, read the whole article to see more questions of this type.