Question

prove that root 5 is irrational number ​

Answer 1

Step-by-step explanation:

$let \: \sqrt{5} \: is \:a \: rational \: number \\ = > \sqrt{5} = \frac{p}{q} \: where \: p \: and \: q \: are \: integers \: and \: q \: is \: not \: equal \: to \: zero \: \\ = > \sqrt{5} = \frac{p}{q} \\ squaring \: on \: both \: sides \\ = > { \sqrt{5} }^{2} = \frac{ {p}^{2} }{ {q}^{2} } \\ = > 5 = \frac{ {p}^{2} }{ {q}^{2} } \\ = > {q}^{2} = \frac{ {p}^{2} }{5} \\ 5 \: is \: divisible \: by \: {p}^{2} \\ 5 \: is \: also \: divisible \: by \: p \: from \\ = >$

Answer 2

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