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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.

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.

Grade:9

1 Answers

Vijay Mukati
askIITians Faculty 2590 Points
8 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.

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