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