Prove that root 2 or √2 …

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Prove that root 2 or √2 is irrational no.

Posted by Uttpan Patnaik 5 years, 10 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 5 years, 10 months ago

Suppose $\sqrt2$ is a rational number. That is , $\sqrt2$ = $\frac{p}{q}$ for some p $\in$ Z and q $\in$ Z. We can assume the fraction is in lowest fraction, That is p and q shares no common factors.

Then $\sqrt2q=p$

Squaring both side we get,

$2q^2=p^2$

So $p^2$ is a multiple of 2,

let's assume $p=2m$

Then, $2q^2=\left(2m\right)^2$

$2q^2=4m^2$
Or $q^2=2m^2$
So $q^2$ is a multiple of 2,
$\therefore$ q is multiple of 2
Thus p and q shares a common factor.This is contradiction.
$\Rightarrow$ $\sqrt { 2 }$ is an irrational number.

1Thank You

ANSWER

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