Question

prove that root 2 is irrational

Answer 1

this is the answer of the question

Answer 2

Hi there !!

Lets assume that √2 is rational

√2 = p/q , where p and q are integers and ,
q ≠ 0 , and p and q are co - prime

Squaring both sides

[√2 ]² = [p/q]²

2 = p²/q²

2q² = p² -----> (1)

So ,
2 is a factor of p² and it also divided p².
Hence , 2 divides p also -----> (2)

So ,
p = 2m

From equation (1) ,

2q² = (2m)²
2q² = 4m²
q² = 2m²

SO ,
2 is a factor of q² and divided q².
So , it also divides q. ------> (3)

From (2) and (3),

2 is a common factor of p and q , which is a contradiction.
Therefore , our assumption was wrong.
Hence , √2 is irrational