Question

Show that 2/5root2 Is a irrational

Answer 1

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$let \: \frac{2 }{5 \sqrt{2} } be \: a \: rational \: number \: \\ \\ \frac{2}{5 \sqrt{2} } = \frac{p}{q} \\ \\ = > 2q = 5 \sqrt{2} p \\ \\ = > \frac{2q}{p} = 5 \sqrt{2} \\ \\ \\ = > \frac{2q}{5p} = \sqrt{2} \\ \\ \\ \\ but \: \frac{2q}{5p} \: is \: rational \: and \: \sqrt{2} \: is \: irrational \\ \\ \frac{ 2q}{5p} ≠ \sqrt{2}$


Our assumption was wrong

therefore,
$\frac{2}{5 \sqrt{2} } is \: irrational$


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✌hope it helps u ✌

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