is not divisible by 5
We will prove that the given statement is true by contradiction.
Let . Assume is divisible by 5. Let,
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 .