Question

3. Prove that the following are irrationals:

$(1) \div \sqrt{2}$
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Answer 1

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

$hence \: \frac{1}{ \sqrt{2} } can \: be \: writen \: in \: the \: form \: of$

$\frac{a}{b} \: where \: a \: b$

(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 2

Answer:

Prove that the following are irrationals:

Step-by-step explanation: