Conjugate Surds

For rational \(p,q,a\) with \(a\ge0\), the conjugate of \(p+q\sqrt a\) is \(p-q\sqrt a\). Their product \(p^2-q^2a\) is rational.

\( \left(5 + 3\sqrt{2}\right) \left(5 - 3\sqrt{2} \right) \)