Show that V3 - 2 is an irrational number,
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Answer:
Let us assume
3
+
2
be a rational number
⇒
3
+
2
=
q
p
, where p,q∈z,q
=0
⇒
3
=
q
p
−
2
By squaring on both sodes, (
3
)
2
=(
q
p
−
2
)
2
3=
q
2
p
2
−2.
2
.
q
p
+2
2
2
.
q
p
=
q
2
p
2
+2−3
⇒2
2
.
q
p
=
q
2
p
2
−1
2(
2
)
q
p
=
q
2
p
2
−q
2
2
=(
q
2
p
2
−q
2
)(
2p
q
)
2
=
2pq
p
2
−q
2
⇒
2
is a rational number ∵
2pq
p
2
−q
2
is rational.
But
2
is not a rational number. This leads us to a contradiction.
∴ our assumption that
3
+
2
, is a ab be rational number is wrong
⇒
3
+
2
is an irrational number
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