CBSE Class 10 maths solutions Real Numbers Exercise 1.3 | NCERT Solutions Real Numbers

Irrational Numbers Defination:

A number ‘s ’ is called irrational if it cannot be written in the form,p/q where p and q are integers and q is not 0.

Before we prove that sqrt(2) is irrational, we need the following theorem, whose

proof is based on the Fundamental Theorem of Arithmetic.

Let p be a prime number. If p divides a^2, then p divides a, where a is a positive integer.

Proving Irrational numbers

00:02 NCERT solutions for CBSE class 10 maths Real Numbers Ex 1.3 Q1. Prove that sqrt(5) is irrational.

00:40 Assume contrary of given statement.

That is sqrt(5) is rational number which can be expressed in the for of p/q.Where p and q are prime numbers.

We get p and q are not co-prime.This bring contradiction to our statement.

02:51 Contardiction to assumption

03:00 sqrt(5) is irrational

03:25 NCERT solutions for CBSE class 10 maths Real Numbers Ex 1.3 Q2. Prove that 3+2sqrt(5) is irrational.

03:35 Assume contrary of given statement.Take 3+2sqrt(5) is rational.It can be expressed in the for of p/q.Where p and q are prime numbers.

05:10 We get sqrt(5) is rational number which is false.

05:20 Thus our assumption is false.

05:25 3+2sqrt(5) is irrational.

05:48 NCERT solutions for CBSE class 10 maths Real Numbers Ex 1.3 Q3. Prove that the following are irrationals :

(i)1/sqrt(2) (ii)7sqrt(5) (iii) 6+sqrt(2)

06:03 prove 1/sqrt(2) is irrational number

06:10 Assume contrary of given statement.Take 1/sqrt(2) is rational.It can be expressed in the for of p/q.Where p and q are prime numbers.

06:55 we get sqrt(2) is rational which is false.

This is because of our wrong assumption.

07:18 Thus 1/sqrt(2) is irrational number is proved

prove 7sqrt(5) is irrational number

07:30 Assume contrary of given statement.Take 7sqrt(5) is rational.It can be expressed in the for of p/q.Where p and q are prime numbers.

08:30 we get sqrt(5) is rational which is false.

This is because of our wrong assumption.

08:57 Thus 7sqrt(5) is irrational number is proved.

prove 6+sqrt(2) is irrational number

09:16 Assume contrary of given statement.Take 6+sqrt(2) is rational.It can be expressed in the for of p/q.Where p and q are prime numbers.

10:09 we get sqrt(2) is rational which is false.

This is because of our wrong assumption.

10:47 Thus 6+sqrt(2) is irrational number is proved

11:00 Prove that sqrt(2) is irrational.

11:21 Assume contrary of given statement.

That is sqrt(2) is rational number which can be expressed in the for of p/q.Where p and q are prime numbers.

13:28 We get p and q are not co-prime.This bring contradiction to our statement.

13:35 Contardiction to assumption

13:55 sqrt(2) is irrational

14:07 Prove that sqrt(3) is irrational.

14:21 Assume contrary of given statement.

That is sqrt(3) is rational number which can be expressed in the for of p/q.Where p and q are

16:16 We get p and q are not co-prime.This bring contradiction to our statement.

16:35 Contardiction to assumption

16:42 sqrt(3) is irrational

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