Question

prove 5 subtrct root3 is irrational

Answer 1

by reading this you can understand.



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Answer 2

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$let \: 5 - \sqrt{3} \: is \: rational \: number\\ \\ 5 - \sqrt{3} = \frac{p}{q} = \frac{integer}{integer} \\ \\ - \sqrt{3} = \frac{p}{q} - 5 \\ \\ \sqrt{3} = - \frac{p - 5q}{q} = rational \: number \\ \\ therefore \: \sqrt{3} = rational \: number \\ \\ but \: we \: know \: that \: \sqrt{3} is \: irrational \: number \\ \\ since \: our \: assumption \: was \: wrong \: by \: assuming \: 5 - \sqrt{3} rational \: number \\ hence \: 5 - \sqrt{3} is \: irrational \: number$
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