Question :

Show that 3 + 5 √ 2 is an irrational number. Is sum of two irrational numbers always an irrational number?Submitted on 3/3/2024 | Answered by Vandana Rana

Answer :

We can solve it using contradiction method.
Let 3 + 5 √ 2 is a rational number,
then 3 + 5 √ 2 = p/ q
3 q + 5 q √ 2 = p
√ 2 = (p − 3 q) / 5 q
Clearly,RHS is a rational number ,but LHS is not.
So,our contradiction is wrong.
3 + 5 √ 2 is an irrational number