Question

# Prove that 3+2V5 is irrational.

Solution Let us assume on the contrary that 3+2/5 is rational. Then
there exist co-prime positive integers a and b such that
3+25
a - 35
=
215=-3
5
=
15 = 9-35
2b
=
V5 is rational
a-36
:. a,b are integers
is a rational
This contradicts the fact that 15 is irrational. So, our
supposition is incorrect.
Hence, 3+2/5 is an irrational number.

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