Question

prove that 1/root2 is a irrational

Answer 1

❣️Hi there ❣️


Suppose
$\frac{1}{ \sqrt{2} }$
is a rational number.
$\frac{1}{ \sqrt{2} } = \frac{p}{q} \:$
, q is not equal to 0 , p and q are integers .

$\frac{1}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{p}{q} \\ \\ \frac{ \sqrt{2} }{2} = \frac{p}{q} \\ \\ \: \sqrt{2} = \frac{2p}{q}$
p and q are integers and q is not equal to 0.

Hence , 2p and q are integers and q is not equal to 0.

= 2p/ q is an rational no.

$\sqrt{2} is \: rational \: no$

It is contradicting with the fact that root 2 is an irrational no.

So , our assumption is wrong .

Hence 1 /root 2 is an irrational no.

Hope it will helpful !!

Answer 2

see the attached file