show that 3+√2 is an irrational number
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Answer:
Let us assume, to the contrary, that 3
2
is
rational. Then, there exist co-prime positive integers a and b such that
3
2
=
b
a
⇒
2
=
3b
a
⇒
2
is rational ...[∵3,a and b are integers∴
3b
a
is a rational number]
This contradicts the fact that
2
is irrational.
So, our assumption is not correct.
Hence, 3
2
is an irrational number.
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Answer:
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