Question

Prove that 3+2root5 is irrational.

Answer 1

let 3+2√5 be rational then
3+2√5=p/q
2√5=p/q-3
2√5=p-3q/q
√5=p-3q/q×1/2
√5=p-3q/2q
since √5=p-3q/2q=p/q √5 is rational but √5is irrational.this is a contradiction to our assumption that 3+2√5 is rational. hence 3+2√5 is an irrational number

Answer 2

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