Thus \(a^2\) is even, and as such \(a\) is even. So \(a = 2k\) for some integer \(k\text{,}\) and \(a^2 = 4k^2\text{.}\) We then have,

\begin{equation*} 2b^2 = 4k^2 \end{equation*}

\begin{equation*} b^2 = 2k^2\text{.} \end{equation*}