Proving Square Root of 2 is Irrational number | Sqrt 2 is Irarational number Proof
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.
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 Prove that sqrt(2) is irrational.
00:21 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.
02:28 We get p and q are not co-prime.This bring contradiction to our statement.
02:35 Contardiction to assumption
02:55 sqrt(2) is irrational.
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