Question

prove that the 1/root 2 is an irrational number

Answer 1

hey dear

here is your answer

< To prove - 1/√2 is irrational number >

Solution



Let assume that 1/ √2 is rational number



Hence 1/√2 can be written in the form of a /b



where a and b ( b unequal to zero) are Co prime no



no common factors other than 1.



Hence 1/√2 = a / b



< opposite side b /a. is rational number >



and b / a = √2



here b / a is rational

number


but √2 is irrational number

This contradicts our facts


so our assumptions is
incorrect


hence 1/√2. is irrational number


hence proved

hope it helps

thank you

Answer 2

Hey !!

Here is your answer... ⬇⬇

To Prove :- 1/√2 is irrational.

Proff :-

$let \: \: \frac{1}{ \sqrt{2} } = \frac{a}{b} \: \: is \: \: rational \: \: no. \\ \\ \frac{1}{ \sqrt{2} } = \frac{a}{b} \\ \\ \sqrt{2} = \frac{b}{a}$
Here contradiction of our supposition..,

L.H.S is irrational no. while R.H.S is rational no.

so, our supposition was wrong..

Hence 1/√2 is an irrational no. --- ( Proved )


HOPE IT HELPS....

THANKS ^-^