# CBSE Class 10-Mathematics: Chapter – 1 Real Numbers Part 11 (For CBSE, ICSE, IAS, NET, NRA 2022)

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## 4 Mark Questions

**Questions**:

Prove that the following are irrationals.

**Answer**:

(i)

(ii)

(iii)

**Answer**:

**(i)** We can prove irrational by contradiction.

Let us suppose that is rational

It means we have some co-prime integers and such that

R. H. S of (1) is rational but we know that is irrational.

It is not possible which means our supposition is wrong.

Therefore, cannot be rational.

Hence, it is irrational.

**(ii)** We can prove irrational by contradiction.

Let us suppose that is rational.

It means we have some co-prime integers and such that

R. H. S of (1) is rational but we know that is irrational.

It is not possible which means our supposition is wrong.

Therefore, cannot be rational.

Hence, it is irrational.

(iii) We will prove irrational by contradiction.

Let us suppose that is rational.

It means that we have co-prime integers and such that

A and b are integers.

It means L. H. S. of (1) is rational but we know that is irrational. It is not possible.

Therefore, our supposition is wrong. cannot be rational.

Hence, is irrational.