Question

Proof 2+ root 5 is an irrational no

Answer 1

Hello Mate!

$let \: x = 2 + \sqrt{5 } \\ {x}^{2} = {(2 + \sqrt{5} )}^{2} \\ {x}^{2} = 4 + 5 + 4 \sqrt{5} \\ \frac{ {x}^{2} - 9 }{4} = \sqrt{5}$

Here, ( x^2 - 9 )/4 is rational number which is equivalent to root 5 but we arrise at contradiction that root 5 is irratonal. So ,

$2 + \sqrt{5} \: is \: irrational \: no.$

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Answer 2

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