Addition Operation with Rational and Irrational Numbers | Irrational numbers proof.

Sum of an irrational number and an irrational number is irrational.

http://www.learncbse.in/ncert-class-10-math-solutions/

http://www.learncbse.in/ncert-solutions-class-10th-maths-chapter-1-real-numbers/

http://www.learncbse.in/rd-sharma-class-10-solutions-chapter-1-real-numbers/

In this video, Irrationality theorem is explained and proof of sqrt(2) is irrational number is illustrated in detail.More emphasis is laid on rational numbers, co-primes, assumption and contradiction of assume statement.One can understand Sum of an irrational number and an irrational number is irrational.

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.

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.

00:02 Q2. Prove that 3+2sqrt(5) is irrational.

00:10 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.

01:35 We get sqrt(5) is rational number which is false.

01:55 Thus our assumption is false.

02:00 3+2sqrt(5) is irrational..

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