Question

Prove that 3+√5 is an irrational number​

Answer 1

let 3+✓5 be rational so

3+✓5=a/b(where b is not equal to 0 and a,b are integers)

✓5=a/b-3

✓5=a-3b/b

here still a,b are integers so a-3b/b is rational and ✓5 is rational but it contradicts the fact that ✓5 is irrational

this contradiction had arisen because of our incorrect assumption so our assumption is wrong

hence 3+✓5 is irrational

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