prove that 7√5 is irrational
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Let us assume that 7
5
is rational number
Hence 7
5
can be written in the form of
b
a
where a,b(b
=0) are co-prime
⟹7
5
=
b
a
⟹
5
=
7b
a
But here
5
is irrational and
7b
a
is rational
as Rational
=Irrational
This is a contradiction
so 7
5
is a irrational number
Let us assume that 7
5
is rational number
Hence 7
5
can be written in the form of
b
a
where a,b(b
=0) are co-prime
⟹7
5
=
b
a
⟹
5
=
7b
a
But here
5
is irrational and
7b
a
is rational
as Rational
=Irrational
This is a contradiction
so 7
5
is a irrational number
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