Question

Prove that
$\frac{1}{ \sqrt{2} }$
is a rational number.
$\huge\bf{Using\:Method:-}$
$\huge\rm\underline\purple{Contridict}$
Note :- Wrong and Irrelevant Answer will be deleted.​​

Answer 1

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To Prove :-

➪ 1/√2 is an irrational number.

Solution :-

Let us assume that 1/√2 is a rational number, so that it can be expressed in the form of p/q , and q≠0 .

Note :- All rational numbers can be expressed in the form of p/q, q ≠ 0.

∴ 1/√2 = p/q

Taking Reciprocal on both the side :

√2/1 = q/p

√2 = q/p

➪ RHS : Clearly, q/p is a rational number, and p ≠ 0.

➪ LHS : But, We already know that √2 is an irrational number, which is not possible.

Note :- Always a rational number must be equal to a rational number only.

Hence, our assumption is wrong.

This contradicts the fact that 1/√2 is a rational number.

$\large\boxed{∴ \: \frac{1}{ \sqrt{2} } \: is \: an \: irrational \: number}$

@SweetestBitter

Answer 2

Answer in the attachment

Hope it helps you