Assuming that is rational. Then, where and are integers and is in lowest terms. This means that and cannot be both even is irrational.
Squaring both sides, we have
Multiplying both sides by , we have . It follows that is even and is even.
If is even, then it can be expressed as where is an integer. Substituting to the equation above, we have which simplifies to.Dividing both sides by gives . This implies that is even which means that is even.
similarly is irrational.
therefore 6 is totally an irrational number .