# The irrationality of $$\sqrt(2)$$
Consider a rational number fully reduced, $$\frac{p}{q}$$ such that $$\frac{p^2}{q^2} = 2$$. Investigate whether $$p$$ or $$q$$ are odd or even numbers leads to a contradiction which shows that $$2$$ cannot be rational.
• $$p$$ and $$q$$ can't both be even, as [...].
• $$p$$ and $$q$$ must both be odd, as [...].
• $$p$$ is even as [...].