Given
is not divisible by 5
Proof
We will prove that the given statement is true by contradiction.
Let . Assume
is divisible by 5. Let,
where
The above equation is a quadratic equation. The roots of a quadratic equation are given by
We know that . If
then
must also
. This means that
must be a perfect square. But this is not possible.
always have 7 in ones place. A perfect square cannot have 7 in ones place. Therefore, n cannot be an integer. But this is contradictory since
. This implies that our assumption that
is divisible by 5 is incorrect.
Therefore, by contradiction we can say that is not divisible by 5
.