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