Question

Prove 3+√5 is an irrational number.

Answer 1

if possible let 3 + root 5 be rational number.then,
(3+root5) is rational, 5 is rational.
(3+root5)-5) is rational.
Root 5 is rational.
This contradicts the fact that root 5 is irrational.
The contradiction arises by assuming
(3 + root 5) is rational.
Hence (3 + root 5) is irrational.