Question

prove that the following are irrational 1/√2​

Answer 1

Answer:

This is the correct answer of your question.

Answer 2

$\huge \mathfrak \red{ÆÑẞWĒR}$

Step-by-step explanation:

$Let \: us \: assume \: that  \frac{1}{ \sqrt{2} } \: is \: rational \: number$

$Hence \frac{1}{ \sqrt{2} }  can \: be \: written \: in \: the \: form \: \\ of \: {a}{b}  where  \: a,b(b \: \red{≠} \: 0) are \: co-prime$

$⟹ \frac{1}{ \sqrt{2} } = \frac{a}{b}$

$⟹ \frac{b}{a} = \sqrt{2}$

$But \: here  \sqrt{2}  is \: irrational \: and  \frac{b}{a}  is \: rational$

$as \: Rational \: \red{≠}\: Irrational$

$This \: is \: a \: contradiction \: so \: \frac{1}{ \sqrt{2} } is \: a \: irrational \: number$

$\pink{i \: hope \: it \: helpfull \: for \: you}$