Grade 910 grade maths

Pls experts tell how to prove root 2 irrational by condradiction. I am getting very much confused proving this , please tell in th easiest and clearest way to uderstand.

Sameer Nayyar

10 Years agoGrade 9

1 Answer

Vijay Mukati

10 Years ago

Let us consider root(2) is a rational,
So root(2) = p/q, where p and q are integers and do not any factor in common other than 1.
so p² = 2q², these means that p² is perfectly divisible by 2 or p is divisible by 2.
that means, p = 2m (let), so from above , we can write as
4m² = 2q² or 2m² = q², which again means that q = 2n,
From the above values of p and q, we conclude that , p and q will have a common term 2, And hence our assumption was incorrect.
Thus root(2) is irrational No.

Thanks.