Question

Prove that 3+√5 is an irrational number​

Answer 1

Answer:

Hello mate here is your answer

let 3+√5 is rational

so

3+√5 = a/b. (where they are co prime)

so √5 = A/B - 3

√5=. A-3B/b

so rational = irrational

this was not possible

so our contradiction is wrong

so 3+√5 is irrational

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Answer 2

Answer:

Let us assume to the contrary that 3+√5 is irrational no.

3+√5 = p/q【where p and q are co prime and q is not equal to 0】

√5=p/q-3

√5=p-3q/q

√5=p-3q

p and q are integers so p-3q is rational

but √5is irrational

so our assumption is wrong

so 3+√5is irrational