3. Prove that the following are irrationals

1.	3. Prove that the following are irrationals
Answer» $let \: assume \: that \: \frac{1}{ \sqrt{2} } is \: <klux>RATIONAL</klux> \: number$ $hence \: \frac{1}{ \sqrt{2} } can \: be \: writen \: in \: the \: form \: of$ $\frac{a}{<klux>B</klux>} \: where \: a \: b$ (b ≠0) are CO prime $\frac{1}{ \sqrt{2} } = \frac{a}{b}$ ${b}^{a} = \sqrt{2}$ $but \: here \: \sqrt{2 \:} is \: irrational \: and \: \frac{a}{b} is \: rational$ As RATIONAL ≠IRRATIONAL $this \: is \: a \: contradiction \: so \: \frac{1}{ \sqrt{2} } is \: a \: irrational \: number$

Answer»

$let \: assume \: that \: \frac{1}{ \sqrt{2} } is \: <klux>RATIONAL</klux> \: number$