Question

prove that 2+3 root 5 is a irrational number?

Answer 1

Let us assume that 2+3√5 is rational

Therefore,2+3√5=p/q where p and q are co-prime and q≠0

3√5=p/q-2

√5=p-2q/3q

So,√5 becomes rational

But we know that √5 is irrational

Therefore our assumption is wrong

2+3√5 is irrational

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