How to prove that√5 is irrational number?
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Proof by contradiction.
Let's assume that is a rational number. Therefore it can be expressed as
where
and
and
are coprime.
Since is divisible by 5, then also
is divisible by 5.
We can write that .
Since is divisible by 5, then also
is divisible by 5.
But if both and
are divisible by 5, then it contradicts our earlier assumption that those two numbers are coprime. Therefore
is irrational number.
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