Proof that square root of prime number is irrational | Sqrt(5) is irrational number proof

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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/

00:02 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.

In this video, Irrationality theorem is explained and proof of sqrt(3) is irrational number is illustrated in detail.More emphasis is laid on rational numbers, co-primes, assumption and contradiction of assume statement.

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.

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