Question

prove that 3-✓5 is irational number​

Answer 1

Answer:

⭐ Answer ⭐

$let \: be \: assume \: that \: 3 - \sqrt{5} is \: rational \\ \\ therefore \\ \\ 3 - \sqrt5} = \frac{a}{b} \\ \\ \sqrt{5} = \frac{a}{b} - 3 \\ \\ \sqrt{5} = \frac{a - 3b}{b} \\ \\ \frac{a - 3b}{b} is \: a \: rational \: number \\ therefore \: \sqrt{5} \: is \: a \: rational \: \\ number \: but \: it \: is \: contradict \: that \\ \sqrt{5} \: is \: an \: irrational \: number \: \\ therefore \: our \: assumption \: is \\ wrong \: and \: \\ 3 - \sqrt{5} \: is \: an \: irrational \: number.$

Answer 2

Answer:

refer to the attachment