Question

what are different methods to solve 3+2 root 5 is irrational

Answer 1

$\huge\mathfrak\pink{ANSWER }$

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To prove: 3+2root5 is irrational

proof:

let us assume that 3+2root5 is rational.

=>3+2root5=a/b

=>2root5=a/b-3

=>2root5=a-3b/b

so a-3b/b is rational but 2root5 is irrational so this contradict our fact that it is irrational.

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$\huge\mathfrak\green{Proved}$