Question

show that 5+ √7 is an irrational number​

Answer 1

$let \: 5 + \sqrt{7} \: \: is \: a \: \: rational \: \: \: number \: \: \: and \\ \: equal \: \: to \: \: x \: ( \: x \: is \: \: another \: \: rational \: number) \\ \\ 5 + \sqrt{7} = x \\ \sqrt{7} = x - 5 \\ we \: \: know \: that \: x - 5 \: \: is \: a \: rational \: number \: and \\ equal \: to \: \sqrt{7} \: so \: \sqrt{7} \: \: is \: also \: a \: rational \: number \: but \: this \: is \: not \: possible \\ so \: our \: assumption \: is \: wrong \: and \: 5 + \sqrt{7} \: \: is \: \: irrational \: number \: .$

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