Question

How to solve 1-root 2 is irrational

Answer 1

Step-by-step explanation:

Let us assume that √2 is rational.

Hence it can be expressed in the form of

$\frac{x}{y}$

where x and y are integers and y not equal to 0

$1 - \sqrt{2} = \frac{x}{y} \\ - \sqrt{2} = \frac{x}{y} - 1 \\ \sqrt{2} = - (\frac{ x}{y} - 1) \\ \sqrt{2} = - ( \frac{x - y}{y} ) \\ \sqrt{2} = \frac{ - x + y}{y} \\ \sqrt{2} = \frac{y - x}{y} \\ since \: x \: and \: y \: are \: integers \\ \frac{y - x}{y} is \: rational$

but this contradicts the fact that √2 is rational.

This contradiction has arisen because of our wedding assumption that√2 is Rational.

HENCE √2 IS IRRATIONAL

HENCE PROVED.

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