Question

$\sqrt{2} \: \: is \: an \: irrational \: number$
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Answer 1

Answer:

ANSWER

Let us assume on the contrary that √2 is a rational number in the form of p/q where 'p' and 'q' are integers and q≠0.

Therefore:

√2=p/q

On squaring both the sides, we get:

=>2=p²/q²

=>2q²=p²-------(i)

It means 2 divides p² i.e it also divides p.

Now:

Let p=2m for some integers 'm'

Putting it in equation (i) we get:

2q²=4m²

=>q²=2m²

=>2m²=q²-------(i)

It means 2 divides q² i.e it aslo divides q.

From (i) and (ii), we obtain that 2 is a common factor of p and q. But, this contradicts the fact that a and b have no common factor other than 1. This means that our supposition is wrong.

It means√2 is irrational number!