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