Question

prove that 3-2√5 is an irrational number​

Answer 1

$\tt \huge \: Hola!$

• ProoF :

$\sf \large \: Let,$

$\mapsto \sf \: 3-2√5 (=x) \: \: is \: \: a \: \: rational \: \: number$

$\: \: \: \: \: \: \: \: \: \: \: \sf \: x = 3 - 2 \sqrt{5}$

$\implies \sf \: 3 - x = 2 \sqrt{5}$

$\implies \sf\frac{3 - x}{2} = \sqrt{5}$

$\sf hence , \: \: \sf \:rational \: \: number \: = irrational \: \: number$

→ But it's not possible

hence,

$\sf { \underline {\boxed{ \tt{ 3 - 2 \sqrt{5} \: \: is \: \: a \: \: irrational \: \: number}}}}$

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HOPE THIS IS HELPFUL...