Question

27. Prove that 3-2/5 is irrational.​

Answer 1

$\sf \: Let \: us \: assume \: 3- \sqrt[2]{5} \: is \: rational \: no.$

$\rightarrow 3 - 2 \sqrt{5} = \frac{p}{q} \\ \sf \: where \: p \: and \: q \: are \: coprime \: factors \\ \sf and \: q \: \cancel{ = } \: 0$

$3 - 2 \sqrt{5} = \frac{p}{q} \\ 2 \sqrt{5} = 3 - \frac{p}{q} \\ \sqrt{5} = \frac{3q - p}{2q} \\ \sf \: but \: \sqrt{5} \: is \: irrational \: no.$

$\hookrightarrow \sf \: so \: it \: contradicts \: the \: fact \\ \sf that \: is \: rational \: so \: our \\ \sf \: assumption \: is \: wrong.$

$\sf \:3 - 2 \sqrt{5} \: is \: irrational \: no.$

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