#### 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