Contrapositive and Contradiction · Challenge problem

Assume $x = \dfrac pq$ for integers $p, q$ with $q \ne 0$

Assume $\sqrt x$ is irrational

Assume $\sqrt x = \dfrac pq$ for integers $p, q$ with $q \ne 0$

Assume $x$ is irrational and $\sqrt x = \dfrac pq$